My 2 week old baby loves to sleep on my chest and I dont mind because I take him off when it's time for bed

But when he does sometimes it's for 2 or 3 hrs at a time (I have nothing better to do right now lol but this isn't about me 🤣) and when he gets off finally his head is all sticky from sweat and I'm worried about him maybe overheating?

He breathes just fine and I make sure we're skin to skin and the fan is on but should I not put him on my chest? Or how can I make it less sweaty??? Could I put something where his head is so it's not against my chest?