i foster young kittens (less than 8 weeks) through a shelter program. basically as long as they're eating and run around occasionally or play with stuff, they're fine. i wouldn't worry about temperature unless they are vomiting or have diarrhea. even then i wouldn't be too concerned as long as he continues to eat. (don't get me wrong, those are bad things, but common and usually easily treated if they go on.)

a healthy 12-week-old should be pretty active I think. but he might have a little bug from being in the shelter, that happens a lot. vaccinations can sometimes slow them down (i don't usually have them that long but that's what i hear). a 12 week old who is eating is likely to get over it fine.

also i think you can feed a kitten as much as he will eat. older cats might have to be limited, but not kittens.

looking forward to pictures