If A Dog Has Diarrhea But Still Drinks Water But Nose Is Dry And Warm?

The nose being dry is usually caused by inactivity (a sick dog is often lethargic and not active possibly explaining how the myth came about and is so misunderstood). So by describing a dry nose is your dog less active than usual would be the question or did you just check during what would be a normal sleep period or just after awakening? Is your dog drinking more or less water than usual or is that the same as always? More or less can indicate a problem. Is your dog eating normally? Is your dog otherwise acting normally?
Diarrhea for more than 3 days or if it is excessive and your dog is likely to dehydrate and you need to see your vet because there is likely an underlying cause that needs treatment. If during those three days there are any other symptoms like change in eating, drinking, behavior, vomiting, fever, ANYTHING, you need to see your vet sooner. If there is anything in the stools like blood, they are black, greenish, yellowish, slimy, gel, or anything resembling parasites you need to see your vet sooner than the three days.
If it is just plain old diarrhea and not excessive with no other symptoms you can try adding some canned pumpkin (not pie filling, pumpkin), and share a small amount of plain yogurt in case they may benefit from some good bacteria in the intestinal tract for those three days. Do not wait longer than three days or if there are any other symptoms.