Is it normal for babies to perspire a lot?

Yes, it is normal as young babies' sweat glands are not fully developed yet. You may notice the head sweats more than the rest of the body. it's because the surface area of the skin in a baby's head is more than the surface area of the baby's body. Do make sure baby's sweating is not due to overheating. Give him/her a warm bath will help him/her to feel more comfortable.