Cheapest thermostat is the reptitemp 500r, around $25. You should only need one though. Then get a dimmer for the cool side. Plug the UTH into the dimmer and the dimmer into the thermostat.

Cardboard over the screen will not help hold humidity, it will suck up the humidity and you will end up with damp cardboard. Go with either aluminum tape, foil or acrylic/plexi glass.