Overheating while sleeping

I have a 9 week old baby girl. She sleeps in her own crib in her own room.

I turn on the ceiling fan every night to help keep air circulating and have the temperature reading at 68-70°F. Baby girl sleeps in a cotton sleeper and has a cotton velcro swaddle on. I put her in bed and when I grab her, she is very clammy and hot, sometimes sweating. In my arms in the room, she does not sweat. The only way for her to not sweat is to have an oscillating fan pointing at the crib.

Could it be possible that the mattress makes her overheat?? She has a “waterproof” mattress my in-laws gifted us. I’ve seen the breathable mattresses that look like a plastic netting and am considering buying one of those. This one she has is a hard plastic, and I’ve put my face up to it and it’s hard for me to breathe through. Not sure what else it could be at this point! Help!!

Link to mattress she has now: https://www.walmart.com/ip/550787919?sid=93db06d2-3aab-43aa-9116-aa8a2fbec9a5