You will know your rat is hot when he lies flat like a pancake or lies on his back and sides with his paws in the air (they dispense heat thru their paws).
If he's in a wire cage, has a fan (make sure he can get out of the fan's blowing path), he should be fine. If he starts showing signs of heat, you can always do things like freeze a small plastic waterbottle, then cover it with a sock, and put it in the cage. He will cuddle up to the coolness.
Dog kibble can be a part of their food, but since it is seriously lacking in Vitamin K it cannot be their proper diet.
The best thing is to try to find good quality lab blocks as they were created as a complete diet for a rat's entire life. You can then supplement with veggies and some fruit and protein.
Stay away from all seed rodent mixes, stay away from Sunseed and Kaytee as well.
about bathing. I only bath rats that are older and need help, or if someone has gotten into something, or possibly a very greasy hormonal buckrat. A rat fully bathes itself many many times in a day and are probably cleaner than us. They do not need baths by you at all.