Humidity in a cageeee? Help? 10POINTS!?

I just purchased a Pac Man Frog (Horned Frog). He's very tiny now no where near full grown I have everything I need for him. My rooms super cold and There's nothing I can do about that..... It's in the basement so i can't keep the humidity in the cage at 80%... I got it to 55% tops... I have a wire mesh top on the cage so What I did was I sprayed the cage just enough and I put plastic wrap over the mesh and a damp towel under the mesh to keep most of it in then On the other side I have a heat lamp to get the temp where it needs to be around 80 degrees but I can't seem to get the humidity correct... any help?