Can my baby wear a hat to sleep?

Can my 3 week old daughter sleep with a hat on? she sleeps in a binet next to my bed in her pjs and a receiving blanket and another lightweight blanket over that and i like to sleep with my fan on so i think that might make it a little more chilly in the room, i feel like she is uncomfortable or shivvering unless i put a hat on her but its hard to tell if she is cold or just being a squirmy baby. But i was told that it is not okay to put hats on babys while they sleep because they can overheat or suffocate?