Hi gtomkins.
Welcome to our Mattress Forum. 
Thanks for sharing your Casper Wave Hybrid story with us - sorry to hear you are sleeping hot on the mattress. But this is no surprise for those that dig a little deeper into temperature regulation issues.
Memory foam (even gel enhanced versions) is well-known for being an issue for those sleeping hot Along with this I’d keep in mind that usually it is difficult to track down temperature regulation issues for any particular person on a specific mattress because there are so many variables involved (including your room temperature and humidity, your sheets and bedding and bedclothes, your mattress protector, or any mattress pads you are using, and where you are in the “oven to iceberg” range) and some people can sleep warmer on mattresses that most people are generally fine with … there is more about tracking mattress temperature regulation issues potential causes ~ Post #2 here (at least to the degree possible for a specific mattress) and the posts it links to that may be helpful.
As this is the most critical issue for you, I’d make sure to also read more about the many variables that can affect the temperature of a mattress or sleeping system in post #2 here and the posts it links to that may be helpful. You may also be interested in the information in post #28 about temperature regulation and mattress microclimate.
Some of the other factors involved in how warm a mattress sleeps are how closely the foam conforms to your body (the more closely it conforms around you the more insulating it is), how soft or thick the foam in the comfort layers are (the softer/thicker it is the deeper you will sink into the more insulating materials), the type of quilting used in the mattress (natural fibers allow for more airflow and humidity control which translates into better temperature regulation), the type of ticking (cover) used (natural or more breathable fibers such as cotton or viscose or even some of the more breathable synthetics will wick away moisture and ventilate better and humidity control is a key part of temperature control), and on any cooling technologies used in the mattress such as ventilating and moisture-wicking materials, heat conductive materials, or phase change materials.
In addition to this … the mattress protector you choose along with your sheets and other bedding and what you wear when you sleep will also have a significant effect on temperature regulation because they can either add to the insulating effect or to the ventilating and moisture-wicking effect of your mattress. Bedding made from natural fibers or viscose materials (like bamboo) will also tend to be cooler than synthetic fibers and linen sheets along with silk are probably the coolest of all the natural fibers for those where the sleeping temperature is a main priority. In many cases changing the mattress protector, sheets, or bedding to cooler versions can make “enough” of a difference for many people who would otherwise sleep hot on a mattress.
Yes, I’d tend to agree …The “hand feel” of most gel memory foam will be noticeably cooler than regular memory foam but temperatures will tend to equalize over time at which point the insulating properties of the foam will become dominant. The amount and type of gel in the foam can affect whether the temperature benefits will last longer or shorter and the cell structure and amount of airflow through foam will also play a very significant role in reducing heat buildup in the material. They certainly have a strong marketing department that stimulates more impulse buying than it provides facts and being transparent about specifics of the componentry that would allow consumer comparisons to similar mattresses and make an informed mattress purchase. Compared to many mattresses made by smaller manufacturers … there is nothing special about Tempurpedic outside of their name recognition and the amount of advertising they do. You can see some of my general thoughts about Tempurpedic in post #10 here and the posts it links to and while for the most part, they do use good quality materials … for most people they certainly wouldn’t be in the best value range compared to many other similar mattresses that use the same or similar quality materials (or sometimes better quality) and are in much lower price ranges.
The mattress itself has five layers of CertiPUR-certified foams (poly and memory foam) of unknown densities. The cooling technology seems interesting and it’s clearly targeting the hot sleepers out there. I have no experience with it and I do not know how well the temperature hydro-powered system works in combination with all other mattress features support/comfort etc. Time will tell. Hopefully other subscribers that have experience with it will see your post and share their experiences.
That said, if you have an excess budget it may be worth trying their cover or chillpad you mentioned, and placing it over your current mattress (or any mattress you find comfortable) to see how it affects your experience on the mattress.
I would not put much stock in the quiz “recommendations” as while in very general terms the quiz may take into account the specific consumer input criteria … there are so many intangible aspects that they cannot be addressed just by giving a “black and white” answer to a criterion. Also, results like these are most likely connected to a smaller or larger degree to commissions received for any sale through their affiliate system. The end-user comfort, support, or longevity of the mattress usually slides towards their bottom line. I wouldn’t recommend considering it anything without first finding the exact specifications of the foams (thickness, density, IFD) and also testing it if circumstances allow.
The most important part of the value of a mattress purchase is durability (which is all about how long you will sleep well) and in terms of durability, a mattress is only as good as its construction and the quality and durability of the materials inside it regardless of the name of the manufacturer on the label.
If you’d really rather purchase something new instead of experimenting to rectify your hot sleeping situation, then I would suggest looking into the offerings of our Trusted Members who we think very highly of and believe they compete with among the best in the industry. They are transparent with their components and have your concerns as a consumer at heart and care more about your health and comfort than their bottom line.
I would always advise before making any mattress purchase that you have a detailed conversation with a knowledgeable and experienced online retailer or manufacturer and provide them with good information about your body type, sleeping style, general preferences and history, some general information about mattresses you have tested and done well with, and any other specific information or circumstances that could affect your choice of a mattress.
Phoenix