if your hands are too hot and you're holding him, i would put him down. chins don't normally like to be held anyway and if you think your hands could be making him hot i wouldn't hold him that often. i usually blow lightly on my chins when they're doing something wrong as a way to say "no!" and they don't really enjoy it so i'm sure he doesn't like it too much.
Blowing on a chin will not help them cool off. Chinchillas circulate their blood through their ears to cool down. That is why red ears is a warning sign that they are too warm.