Sit down and have a good talk with it.
Let your pet sleep in bed with you tonight, under the covers.
Give it milk and see what happens
DO NO feed your pet milk. Unless it's the milk from the mother of the pet.
Pretty much what licenseexpired said, except in our case we don't let the cat have any.
Most mammals aren't supposed to have milk after they are weaned. Most of them like it, but it isn't good for them. (Including humans)
Still an awful lot of them are lactose intolerant, and they can get what milk gives them without consuming milk products.