Dubious of wool filling and heat retention?

After needing to get rid of a memory foam mattress due to being too hot, im dubious about a spring mattress that contains wool and/or hempure over cotton/polyester as i feel wool/hempure maybe hotter than cotten/polester when sleeping. They say that wool draws moisture from you when sweating whilst sleeping to keep you cool (but isnt that why we sweat to cool our bodys down in the first instance?) but i wont be indirect contact with the mattress anyway as i use a mattress protector. can you confirm if a wool/hempure bed or one with cotton/polyester is cooler to sleep on please?