If your house temperature is below 75* normally then you will probably need a low wattage heat lamp or a space heater for the room. The only downfall to heat lamps is that they sacrifice humidity which is already hard to maintain in a glass tank.

Please get a reliable digital thermometer like the one I mentioned so you can actually see what your temps are. Completely forget what those dial thermometers say.

You need to know the temperature on the floor right where the UTH is. Since you are not using a thermostat, it is probably hot enough to cause a burn. They run up to 120* unregulated and if your snake sits on that too long, it will cook itself. So yes, you need to be aware of that temperature.