How to make a basement warmer?
I helped a friend of mine renovate his basement. We installed these raised floor tiles with carpet and pad over them. This made the floor much warmer, especially when going barefoot.

We also put up 2"x4" wall frames around the perimter wall (along with some interior walls) and insulated them. Then we drywalled over them. This reduced the floor area slightly, but it was worth it.

The basement is now typically warmer than the main floor. However, all moisture issues need to be reolved correctly first, or you'll have issues with the wall system.