It is like that when they first wake up and when they are sleeping, then if it is like that after they have been up for a while, then there is a chance that the pup is sick. You should take him in to be seen by the vet. Hope this helps, good luck to you and the pup.
If a dog has a warm or a wet nose, that does not necessarily mean that it is sick. A dog's nose does not always have to be cold and wet. After resting, sleeping, or just lying around the house being lazy all day, a dog's nose is often warm and dry. This also applies if the dog has not recently licked or used his nose for anything. If the dog's nose is constantly warm and dry, this may indicate that something may not be right with its nose and you should consider taking the dog into a vet. Generally, a dog with a warm, dry nose is generally not a sick dog.
Dry or warm nose in dogs is not indication of any health issue. Dogs nose can be warm after waking up in the morning. Some breeds of dogs have more dry nose than other. Dogs nose also become warm when they get fever. Fever in dogs can be due to many reasons. When dogs get fever or any other illness, they show some signs like loss of appetite, weight loss and lethargy etc. If your dog has warm nose and does not have any signs of illness then no need to worry. In fact you have to note signs of illnesses not nose conditions. Dogs can be ill with cold nose and healthy with dry nose.
It should be when it is sleeping or just waking up....if not it is probably sick...I would take it to a vet