Baby + Nightly Sweats

Darleesia
My house is always pretty cold but Ace (3 weeks old) sweats in his sleep (his clothes are soaked & hair is wet too). I keep him in sleepers and/or pants and onesie because I know my house is cold. When he wakes up wet I may even put a hat on him since his hair is wet & so that he won't get sick! 
Any advice for me? I have not a clue.