The Doctor is astounded at how he just can't keep away from her.
It's nothing conscious. He doesn't do it on purpose, it just happens—he's fiddling with the console and she pops up next to him to watch like she always does, and before he knows it he's guiding her hands around the bits and bobs and explaining their functions. The look of both concentration and fascination on her face warms him from head to toe every time.
Or, on other occasions, they'll be walking through some far-flung civilization admiring the flora and fauna and he'll realize that they had begun to walk arm-in-arm at one point and he hadn't even noticed. He doesn't mind the proximity as much as he probably should.
It's like he's physically incapable of keeping himself from touching her, even innocently, and while it's not the most distressing thing he's ever encountered it does befuddle him.
Another habit he's taken up is the kissing—little pecks every now and again, chaste things on the hand or cheek or forehead. Sometimes it's the relief of seeing her alive—he did watch her die twice—and other times it's completely out of the blue. She'll just be pottering around in the kitchen with her soufflés and he'll announce himself by leaning curiously over her shoulder, kissing her on the cheek and asking what's burning. (He usually gets a swat for that but it's worth it.)
Naturally he doesn't afford himself the time to think about it too deeply. He's afraid of what he might find, and the consequences of it.
Everyone he's ever loved has died, or been left behind, or simply left. Admitting tolove of any kind would be making a commitment, and it's still much too soon to open himself up so fully.
But as he looks down at Clara, and she looks back up at him and grins, he lets himself smile back.