Try to eat cool stuff, put sandwiches in the fridge for a few minutes, etc, stay out of the heat, use A/c. This use to happen to me all the time in Az, our summers were between 120 - 130 and you were lucky if it got down to 100 by midnight.
Nibbling is good, also grab one of those electrolyte drinks. Yes, they are major calories, but they can do stuff water just can't when it's that hot. If you start to feel over hot, and really can't eat. Try a few sips of one of those. This sometimes is your body’s way of telling you. It's sweating too much, and losing stuff it needs and it doesn't have what it needs to replenish and be normal. I've always found if I drank a cup of one of those, my appetite would come back with in about an hour. But really try to stay as cool as possible, but do keep an eye on your body and make sure you don't sweat too much. Since the heat starts early it's nothing to sweat all stuff your body really needs out. Espeically if you don't have A/C.
Good luck,
Kit