Maybe add radiant heating before putting the floor down? Some engineered floors are suitable for use over radiant heat, I think.

We have a cold crawl space under our flooring. Put engineered wood (hickory with no edge bevels) over a 1/4 inch cork underlay. Never noticeably cold and easy on the feet. My wife loves the floor. Warning: dropping knives or cast iron pans will damage engineered wood. We've done it! Also my wife knocked over a whole bottle of super glue on it and didn't wipe it up (she didn't notice it). That was/is a mess. Much scraping and still there are scars. I will have to sand and refinish the spots at least to make it look decent.

Thank you MiaOKC and nerdyshopper! Nerdyshopper, where did you buy the 1/4 inch cork underlay? Is it glued down or floated? The Radiant heat will not work with the Brazilian Cherry Engineered Wood Floors I want to use so I will see if the store can put down the cork underlay instead.

Nerdyshopper, does the floors feel solid since my floor muffler plus under my engineered floors also felt like a solid floor but I need more insulation.

I bought then online from Ifloors.com if I recall. They are cork tiles about 3 feet long by 18 inches wide. They are laid side by side with no adhesive. Might have been 5/16 inches thick. I suggest you look over their site and see if you can find the stuff. It may be in the engineered wood section of the site since that is what I installed. I didn't buy the flooring from them because I got a lower quote from a different online vendor at the time.

Thank you so much nerdyshopper for the information.