baby sweats during naps

Madeline
My son is a year old and he sweats every time he takes a nap or goes to sleep. When he takes a nap at home he just where's a tshirt and at night I have a light blanket on him, the ceiling fan going and a tower fan, and I put him in light pajamas. But he still sweats so much that it wakes him up. We live in south Texas so it's pretty hot right now but we keep our ac at 70 and leave all the fans on. I feel so bad because he woke up from a nap drenched in sweat. I don't know what to do to keep him from sweating so much. Does anyone else have this problem?