Variation of Chapter 14 of Eliezar Yudkowsky's Harry Potter and the Methods of Rationality. Because, really, McGonagall is smarter than that.
"So it is," Professor McGonagall said, "but I do have a very special something else to give you. I see that I have greatly wronged you in my thoughts, Mr. Potter. Please wait here."
She got up, went over to the locked back door, waved her wand, and a sort of blurry curtain sprang up around her. Harry could neither see nor hear what was going on. It was a few minutes later that the blur vanished and Professor McGonagall was standing there, facing him, with the door behind her looking as though it hadn't ever been opened.
And Professor McGonagall held out in one hand a necklace, a thin golden chain bearing in its center a silver circle, within which was the device of an hourglass. In her other hand was a folded pamphlet. "This is for you," she said.
Wow! He was going to get some sort of neat magical item as a quest reward! Apparently that business with refusing offers of monetary rewards until you got a magic item actually worked in real life, not just computer games.
Harry felt a small but genuine surge of disappointment when he reached out his hand and the Deputy Headmistress placed the pamphlet in it, while keeping the necklace deliberately out of reach.
"Er…" he started. "What is it?"
Professor McGonagall took a breath. "Mr. Potter, this is an item which is ordinarily used to help students who have shown themselves to be highly responsible with difficult class schedules. And that very infrequently." McGonagall hesitated, as though about to add something else. "I must emphasize, Mr. Potter, that the school's possession and use of this item is secret and that you must not tell any of the other students about it. If that's not acceptable to you, then you can give it back now."
"I can keep secrets," Harry said. "So what does it do?"
"This is a Spimster Wicket. Officially, it is used to treat a rare, non-contagious magical ailment called Spontaneous Duplication, which you have contracted. You have no reason to discuss Spontaneous Duplication with anyone, but you also have no reason to treat it as an awful secret. Spontaneous Duplication is not interesting. Do you understand, Mr. Potter?"
Harry nodded, his smile widening. He sensed the work of a competent Slytherin. "And what does it do?"
"It's commonly called a Time-Turner. Each spin of the hourglass sends you back one hour in time. So, if you use a Spimster Wicket to go back two hours every day, you should always be able to get to sleep at the same time."
Harry's suspension of disbelief blew completely out the window.
"You're giving me a time machine to treat my sleep disorder?" he asked slowly, but with a mounting edge of hysteria. "You're giving me a TIME MACHINE to treat my SLEEP DISORDER? YOU'RE GIVING ME A TIME MACHINE IN ORDER TO TREAT MY SLEEP DISORDER?!"
Harry was staring intently at the necklace in the Headmistress's hand, as if she was casually dangling a live bomb over her desk. Well, no, not as if it were a live bomb, that didn't begin to describe the severity of the situation. Harry stared at the necklace as though it were a time machine.
"No, Mr. Potter, of course not. Don't be absurd. Time-turners are rare, extremely expensive, and breakable. And paperwork required by the ministry if one is damaged or misused is substantial. I am not giving you a time machine at all. I am giving Madame Pomfrey a time machine to treat your sleep disorder."
"Oh," Harry said. This was, he suddenly realized, incredibly disappointing. The more he thought about it, the more intensely disappointing it became, in fact. Finding out there were time machines and not having one was like finding out that there were interplanetary spaceships and the last one took off an hour ago. It was disappointing on a scale whose only possible response was immediate and concerted effort to acquire a time machine. The existence of time machines raised so many questions, created so many possibilities. Why, if you could transfer information iteratively, you could prove that P = NP. You could solve any arbitrary problem which had solutions that were easy to test but large in number.
Assuming we didn't destroy the world, of course. inserted Harry's Ravenclaw side. Time reversed ordinary matter looked just like antimatter. One kilogram of antimatter encountering one kilogram of matter would annihilate in an explosion equivalent to 43 million tons of TNT. Harry himself weighed 41 kilograms…
Really, now. the voice Harry identified as his inner Hufflepuff said. If they were THAT dangerous, children wouldn't be allowed to use them.
At least, Slytherin suggested, it would have only been allowed once, after which time it would no longer be an issue, since there would only be a smoking crater where Scotland used to be!
That's true, Ravenclaw said. Given that we grew up on the British Isles, and Time-Turners have been in use at Hogwarts during that span, it's very improbable that any single use of a time-turner would cause the destruction of large portions of the British Isles. If catastrophic matter/anti-matter reactions were possible at, say, 1% of Time-Turner activations, and there are three students at Hogwarts using a time-turner once per day on average, the number of possible Harry Potters who survive to age 11 in a world that contains a reasonably intact Scotland would be dwarfed by the number whose worlds do not contain Scotland. This isn't proof, of course, but it's fairly strong evidence that routine time-turner use is unlikely to cause catastrophic geography annihilation.
This would likely have continued for a while, but fortunately Professor McGonagall chose to speak up again.
"You'll need to report to the infirmary each day immediately after lunch, before your first class of the afternoon. Madame Pomfrey will provide you with a Spimster Wicket, which you will use to move backward in time two hours. You will then spend those two hours quietly entertaining yourself in the infirmary, not bothering anyone. I suggest you bring a book, or some schoolwork."
"Couldn't I just hold on to it myself?" Harry suggested. Given the existence of time machines, and the reasonable probability that they could be used safely, the prospect of actually having one in possession was irresistibly tempting. Not that Harry was trying hard to resist. He would need to investigate buying one straight out with his Gringott's funds, if possible, but simply borrowing this one would certainly be more convenient. Actually, purchasing one, if possible, should be prioritized. Or purchasing several. It was worth any monetary price, because with future information you ought to be able to generate arbitrary amounts of wealth quickly via simple stock speculation. Or, for that matter, gambling. Horse races completed in less than an hour, and time-turners could obviously move you backward multiple hours, so picking winners would be trivial.
"No, Mr. Potter. Besides the expense, time-turners are a very limited resource for Hogwarts, and other individuals may need to use that one. Also, there are known side-effects to overuse of time-turners, and Madame Pomfrey will be observing you to ensure that no harm comes to you. It's all detailed in that pamphlet."
Harry quickly leafed through the booklet.
"Malnutrition. Dehydration. Sleep deprivation. Hallucinations. Paranoia. Goniphobia. Forgetfullness. Physiological addiction. Psychological addiction. Impaired judgement. Delusions of grandeur… "
"You see, Mr. Potter," the headmistress suggested primly, " why I believe we need expert observation. Imagine how difficult it will be to distinguish between your normal mental state and delusions of grandeur."
"Ha. Ha. Wait, canine trauma? Using a time-turner causes you to be mauled by dogs?"
"Only in very unusual circumstances, after prolonged use. If you have reason to believe you are being stalked by extra-temporal predators, please notify Madame Pomfrey immediately. Likewise if you start seeing blue telephone boxes in odd places, but that's also extremely unlikely. Now, then, we need to get you in synch for the start of the semester, and allow you to conduct an extensive exercise in the misuse of time travel which will simultaneously demonstrate your largely good intentions and your inability to act with restraint and good sense when provided with the means to travel in time."
"What?" Harry said, both confused and outraged. "I haven't done anything with time travel at all, yet, much less misused it! You don't have any reason to think I'll be irresponsible with it!"
"On the contrary, Mr. Potter," Minerva said cheerfully. "I have excellent evidence that you are about to use the ability to magically bend time in an incredibly frivolous manner. It has, after all, already happened from my perspective, even if it hasn't from yours. Now, I believe we need to send you back five hours this one time, correct? That should bring your sleep cycle to the right place, and in the future two hours will suffice to maintain it. Enjoy those five hours. It is an opportunity that will only come to you once, after all. And will earn you a stay in detention commensurate with the time I'm about to spend filing paperwork to the Ministry of Magic for your misuse of a time-turner. Something for you to look forward to, as it were. Five spins! Off you go!"
This is completely unfair. Slytherin objected. We haven't done anything wrong, and we're being given detention? Besides, now that we know we'll be caught, obviously we aren't going to do anything improper. We'll just sit quietly and read a book for five hours. That'll teach her!
Our morning has been pretty surreal, Ravenclaw said. In ways that are best explained by us misusing time travel. And McGonagall claims we've already done it. If we don't abuse these five hours in punishable way, we could create a paradox! We might BREAK TIME! Is avoiding detention worth that?
Oh, shut up, Gryffindor inserted. This is going to be awesome, and we have to do it right now. It's totally worth it, we know we're going to do it, and everything else is just pre-facto rationalization, which we might as well skip since we already know how it's going to turn out. Game ON!
Harry Potter gave the Time Turner five spins. He couldn't accomplish anything stuck here in the future.