Are they stone walls? Is there any framing or are they bare walls? Sprayfoaming or putting up some kind of vapor barrier foam boards would help a lot with the dampness. A ceiling fan would help push the heat down and circulate the air as well. It sounds like maybe an HRV would also probably help. Honestly though, insulation can make a massive difference. If you're going to do anything, I'd start with that. Any kind of heating or dehumidifying system isn't going to work as well without insulation and you'll just be paying out the ass in energy costs.