If you use a cot mattress protector it will not be fully breathable, it can't be of it would not protect the mattress. A waterproof protector will increase the chances of your baby overheating as no air will get to your baby.
If you have an Easychange® cot mattress the core of the mattress is protected fully by a separate waterproof machine washable wipe clean Safetex cover.
Around the top of the Safetex cover is a perimeter zip that takes a Coolmax© and MaxiSpace topper.
The Coolmax© topper will wick away excess heat, the MaxiSpace backing will disperse it . This topper holds a huge amount of air and offers maximum breathability.
You also get a second topper, a godsend for those inevitable night-time accidents;-
Zip off the wet topper and zip on the dry one ( wipe the Safetex protector, in the unlikely event the spills have gone through.
https://www.cotmattresscompany.com/collections/cot-mattresses/products/reassurance-coolmax-easy