My hamster always had a wet belly, it's nothing to worry about, I still don't know why he had a wet belly, wether it was sweat or not, but he was fine all his life. It could just be because he uses his bed so much and it starts getting damp, I always kept Valentines bed for more than a week and changed the rest of his bedding, if you do the same this could also be why, but I wouldn't panick to much. It probably happens when you are getting up to the day you are due to clean out the cage? It could also be because his fur is very greasy, if his fur is greasy and you are worried than just change the bedding more frequantly, also, if the fur is actually greasy and not wet, which could be an easy mistake to make, than it could just be a gene for the coat type to have greasy fur.
However, if he is eating, drinking and cleaning himself normally, than don't worry, it's probably one of the things I mentioned, if you notice him becoming lethargic, than definatly take him to the vets, I don't think he has an illness though

Good luck

xxx