Hey tisman91,
Well, interesting about the cover, misleading and mattress industry sometimes go hand in hand, hence this is what makes TMU so great.
You mention that there is a high probability that this cover “may be the culprit” of the heat issues. I don’t see any data or facts that confirm this being the key reason. I am not saying you are wrong, just as an unbiased participant, and looking at the total scope, not sure is the main reason. But as far as mitigating the heat issues of your very comfortable mattress.
Regarding the solution, can you replace the cover, well I guess technically you can, but this is a non-zipper cover so you would be manually changing the by cutting it off or cutting the top part off, and then lose the warranty. Then you would buy a cover on the open market as most traditional manufacturers don’t sell "replacement covers.
Regarding what is the best fabric replacement to look for here are some good posts about cooling and fabrics, etc etc. Some of this information may be duplicated but worth getting caught up on.
This post #29 has some good information about heating/cooling/climate of the mattress and associated fabrics.
Additionally, the first half of this post #7 has some great links to more information.
All of this, of course, is separate from any environmental conditions in the bedroom (temperature and humidity levels with higher humidity adding to the perception of heat), on the physiology and tendency of the person themselves to sleep warmer or cooler and where they are in the “oven to iceberg” range, and on their weight and body type which will affect how deeply they sink into the foam layers of the mattress. And also the clothes that you are wearing to bed, as these are closest to the skin, and effect moisture wicking, and breathability.
Hope this helps, some of the members of this site do sell mattress covers and can help you get a new cover or mattress pad if you choose to remove your existing cover.
Thanks
Sensei