I don’t know the building code for your area or if it would even work with the other stuff in the area, but the idea is to lay at least 2x2’s every 16", put Styrofoam between the 2x2’s, lay plastic or tyvek or some vapor barrier over it all then lay down plywood and carpet on top of that. It’s a lot of work to retrofit this into an existing space, but if you’re starting over, it may be worthwhile.

I had a townhouse on a concrete slab and in the winter, the cold would transfer through the concrete to the point that when it was below 0F, the water lines running through the concrete would freeze up.