In the absence of other symptoms, the nose is a sensitive barometer of the nasal sweat gland activity, and a dry nose can indicate that a puppy is not in an active sweating phase.
Dogs have sweat glands only on their nose and footpads, so the cooling system of dogs also requires panting to help dissipate excess internal heat. If a puppy is sweating, its nose will feel cold and wet. If you feel its pads, they will often be damp, and they may even leave footprints on a floor. If a puppy is not sweating, its nose will feel dry and sometimes a bit warm. This is normal. Sweating can be associated with overheating, but can also be triggered by activity and stressful events.
If a dog is running a fever, there will be other signs such as lethargy and reduced appetite. Core body temperature elevations often lead to significant panting, lying down with the legs spread out, and an elevated heart rate. An ear or rectal thermometer can quickly confirm the presence of an elevated body temperature. A puppy will often have very warm ears during fevers since the blood vessels in the ears are dilated (vasodilation) as another effective cooling pathway. Feet can also feel warmer than normal due to the same mechanism. In short-coated, light-haired dogs, the ears may even have a reddish appearance because of the vasodilation.