What Do I Feed A Dog That Has Diarrhea And A Dry Hot Nose?

Ideally you'll have your vet check things out as soon as possible if things don't calm down soon. You can boil some skinless boneless chicken breast and some rice or even try adding some canned pumpkin to your pets food if you don't think anythings wrong. Just watch carefully and visit your vet when needed. You may also want to consider the possibility of parasites.
If your dogs nose is dry it's probably not to active when you're checking :-). See if you can get your dog to play a quick game and it'll probably ease your mind :-).

Plain white rice and extra lean ground beef. Not to much though base it on the size of your dog. And not for more then a few days if it is not helping go to vet