When a cat is febrile they can feel hot to the touch. Though this is not an accurate way of assessing if they have a fever. I am often surprised in practice at the actual temperature of a cat that I thought felt normal and has a fever. Also the opposite occurs--the cat feels warm and temperature is normal. The nose is not an accurate way of determining temperature either. It can become warm in a healthy, non-febrile cat. Do NOT give your cat Tylenol--this is acetaminophen and it toxic to cats. It is never a good idea to administer any medication to your pet without consulting with your veterinarian. Also the non steroidal anti-inflammatories can decrease a fever but do not treat the underlying cause--so the fever will likely return.