If your concrete floor is in good shape I'd suggest subfloor tiles (see
https://www.homedepot.ca/en/home/cat...face-prep.html) -- they're pretty easy to install (and uninstall) and don't require special tools or skills, especially if it's just a small space.
Also, instead of poly/plastic wrap, I think hanging some thicker curtains from the ceiling joists might help as well.