I want to buy a Ghostbed memory foam mattress and then separately buy one of tempur-pedics replacement covers from their new Breeze line to cover it. They are supposed to have incredible cooling properties. If they both have a 13" thickness the cover should fit right? Has anyone ever done something like this, or do you have an opinion on creating this "frankenstein" mattress from different brands? Links to both are below. Thanks in advance!

https://www.ghostbed.com/products/ghostbed-luxe?irclickid=3nL3Fo0r%3AxyLWNO0MKVSfWfHUkE0hty7yw0yXY0&irgwc=1&partner_id=1404203&utm_campaign=582113&utm_medium=referral&utm_source=impact

https://www.tempurpedic.com/bedding/mattress-replacement-cover/v/3262/