Not sure how cooling or where you want to go with it, but I bought this one, and it works really well. It covers my 13.25 in mattress and 2.5 in topper combined, and has a super good elastic band that holds everything tight together and nothing shifts.
https://yawnder.com/product/2-5-inch-activedough-mattress-topper-cbd-oil/
this is the topper I have. It did not come with a cover, so I got a this encasement to cover the topper (https://www.amazon.com/gp/product/B082MGNX77/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1). I literally went overboard. I took my old mattress protector, and covered my box springs with it. Covered the topper, Covered the mattress with the BB 5 side wp cover, then covered all of it with the sleep zone (https://www.amazon.com/gp/product/B08ZJ7FDZT/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1) it fits so tight and snug that it doesnt allow the topper or anything to slide around and stays in place. All in all it works perfectly for me. Everything is protected.
I honestly really cant say. I knew I wanted to cover my topper to make it easier to rotate my mattress or flip it if the ultra firm side was too firm. So I got this topper encasement to make it easier to handle the topper. I figured since it is made with the cooling technology fabric, it couldnt hurt. I am crazy about covering things. I put a mattress protector on my box spring, my mattress and the topper, then I covered the topper and the mattress with another cooling mattress cover(https://www.amazon.com/SLEEP-ZONE-Athlete-Grade-Overfilled-Ergonomic/dp/B08ZJ7FDZT/ref=sr\_1\_7?crid=2AVW43HLUF1GS&keywords=sleepzone%2Bcooling%2Bmattress%2Bpad&qid=1683146513&sprefix=sleepzone%2Caps%2C108&sr=8-7&th=1 ) as my thought process was it will keep everything in place. It does! Then I have my deep pocket fitted sheets and flat sheet and duvet/comforter. My pessimistic side says, if I have all the sheets covering the "stack" can the cooling stuff really work. I really dont know, but I am not sleeping hot, and all of my covers fit nice and work together. I suppose I could take the theory, if you have a mattress stack with varying levels of foam and springs, that very dense bottom foam is part of the firmness of the mattress stack even though it is at the bottom. So perhaps all the cooling covers and fabrics are making the whole setup cooler than it would be without. What I do know, the cost for all the components, the sleep zone protector, the subrtex encasement, Brooklyn Bedding mattress protector (directly on the mattress) and the protector on the box springs combined were less than $125. It wasnt enough to change my life, so I just did it. And it is working for me, hard to image it would work against me or anyone else for that matter and all my components are protected even if some might think it is overkill.