welcome to the hobby and congrats on your adoption. i wouldn't say your new BP is favoring the cardboard box on the cool side. he's probably just be over there b/c the UTH is way too hot (and dangerous) b/c it's 100degrees. even if u didn't have a hide on the cool side, i bet he woulda been over there in the corner or trying to burrow under the water dish. appropriately sized identical hides would be better and would encourage better thermoregulating b/c a BP wouldn't be able to choose a favorite hideaway b/c of size, shape, texture, etc.
keep your UTH unplugged, not just at night, until u can get a thermostat. 100degrees day or night is dangerous. it would also be a good idea to put your lights on a rheostat/dimmer.