This story occurs in the universe of s/5782108/1/Harry_Potter_and_the_Methods_of_Rationality, diverging in Ch. 101. It contains spoilers for that story through that chapter, and is unlikely to make much sense without having read the same.
It's intended to be a darker, more pessimistic interpretation of the story.
Harry was holding his breath while feeling his heart pounding. He was invisible, in Dumbledore's office, nearly panicking any time the old wizard glanced in his direction. He silently watched the clock on the wall, it was almost time.
He then pulled the wand from his pocket, extended the tip just millimeters outside the cloak, and touched it to Fawkes' claw as gently as he could. He began to concentrate.
Ten minutes later he finished: Fawkes was transfigured into a small diamond. As he pocketed the diamond with one hand, he activated his time-turner with the other... and ran through the door just as Professor McGonagall opened it and walked through, followed by invisible one-hour-younger Harry. Younger Harry paused in front of the doorway until it closed, blocking any other invisible time travelers from passing through without causing a paradox.
Older Harry sat on the stairs, pulled the cloak off of his head. He removed the diamond and sat it next to him. "Finite Incantatem" he whispered.
"Fawkes, I'm sorry for abducting you," he continued whispering, "but I really need you. It's a matter of life and death. Will you help me?"
The phoenix paused for a moment, then nodded slowly.
"Then take me to The Hall of Prophecy in The Department of Mysteries." In a flash, they had arrived in a room filled with shelves stacked floor to ceiling with glowing white spheres. Harry then used his time-turner to go back two more hours.
Harry drew his wand, casting his patronus as quickly as possible. He then instructed it "In a few minutes, a prophecy will arrive in this room. I want you to do whatever it is you do to find people to find where that prophecy came from before arriving here." The figure nodded and walked through the nearest wall.
Harry and Fawkes waited silently. About a dozen spheres floated over to where Harry was standing and arranged themselves in front of him. "What?... Thats... I should really come back and watch those when I have more time."
After what seemed like much longer than a few minutes, a new white sphere materialized and floated onto one of the shelves. The patronus returned a fraction of a second later. "Did you find it?" The patronus nodded. "Okay, I want you to show Fawkes the way. Fawkes, follow him, then come back and get me." And they were off. And a moment later, so was Harry.