The lid is actually not screen but small metal bars, with two flaps that open so you can reach inside without opening the whole thing.

I've got dry towels over the lid now. M'thinking of covering it with aluminium tape on the inside (for heat reflection) and black tape on the outside (for looks).

Worth a shot?

I bought a 150watt heat bulb and the temp on the cold side is climbing steadily... Nearing 78 now... Haven't seen too much of an impact on humidity yet (went down from 63% to 61%). My water bowl is pretty near right smack under the lamp though, so that may be why.