I think with dogs it's less to do with the air temp than the ground temp since paws and belly are where they expel most heat from. The tile floor that your pooch rests on is probably several degrees cooler so he's probably fine. Have you considered shaving a patch on his stomach so that he can get even cooler when he lies down? It wouldn't affect the way the rest of his fur on his body looked and he would be more comfortable if heat is really that big an issue.
