Wow, what a tough situation to be in! I feel for you!
My first suggestion would be to go back and talk to the day care. Explain the situation to them again, in a calm, non confrontational manner, and ask them for their support and advice. It seems to me that they really need to be supporting you in this and not letting him sleep so long. I've worked in day care, and we never let kids sleep for 3 hours at that age, ever. 2 hours was about the limit, no more than 2 1/2 hours because the other kids were up, and we had a schedule and routine. If we let a child sleep that long, we ALWAYS got complaints from the parents. Part of the job of the childcare is to work WITH the family, not against them; it's their job to support you.
Also, if you think part of the problem is the light, maybe you could darken his room somehow. Could you get heavy blinds or curtains to make his room very dark so maybe it's easier to sleep, and not so bright? I know kids at that age can be afraid of the dark, so you could invest in a nightlight if you don't have on already to help ease any lingering fears. Maybe adding a small fan would help with heat.
About dinner, I wouldn't worry to much if I were you. My appetite goes down in the heat too, so no worries. He'll eat when he's ready. He won't starve himself. Just continue to offer him food at regular intervals and he'll be fine.
He may be going through a growth spurt and his sleep needs may be changing, so as odd as this may seem, maybe you could try shifting bedtime a bit earlier instead. He may be overtired by the time you are getting him to bed, hence too overstimulated to sleep, so maybe shifting bedtime 15 minutes to half an hour earlier might do the trick.
I hope this helps. As my mom always says, This Too Shall Pass! and he'll be on to another phase. Just remember to breathe, take a step back and relax. Hang in there mama! :)