Q. Dog has diahhrea, warm dry nose
A. The diarrhea could be caused by any number of things; intestinal parasites, a bacterial infection, even being constipated will sometimes manifest as diarrhea because liquid feces is all that will get by the impacted fecal material. The warm, dry nose probably doesn't have anything to do with the diarrhea, it just means the dog's nose is warm and dry.
It could be as simple as a dietary indiscretion, meaning she might have gotten into the trash and eaten something that didn't agree with her. If your pet is otherwise feeling fine, eating, drinking and urinating, try taking away all food, treats included, for 24 hours. S/he can still have water. This will give the gut a chance to rest. After the 24 hours are up, introduce just a tiny amount of normal food. Wait an hour and give a little more. Keep doing this until s/he has had her normal amount for the morning. However, if s/he continues to have loose stool, or starts vomiting, loses her appetite, acts lethargic, and/or develops a fever, get her in to be seen by your vet right away as this could indicate a more serious problem.