Well try a test run for 24-48 hours to figure out what your temperature swing is. Like run the light on at night and the heater on in the day? That may work to bring you to a normal temperature range. I assume insulation is out of the question? The best you can do it to warm the whole room and see how it goes in the test run. I'm sure you can find a balance that would work.

You never know until you try.