I would HAVE to have padding of some kind underfoot. Too much time on my feet and my back starts groaning and my plantar faciitis starts burning. We replaced the carpet in our family room several years ago. We got the best pad with a middle-of-the-road carpet. I can definitely tell the difference between the different grades of pads in our house when I walk in that room.
I've heard that there's a bamboo wood flooring that you can install with a pad or something somewhat squishy underfoot, it's not as hard as wood or concrete. No idea if it's warmer, though.