Carol’s concept is an excellent one for a hot climate summer box. White surface facing the sun, insulation underneath, and an air gap between the insulation and the house. The white surface reflect away most of the sunlight, so the outer surface stays as cool as possible. The insulation keeps the heat from being transferred to inside surface. The air gap serves as an insulating layer and as a chimney to cool the inner layer of the insulation, removing whatever heat gets transferred to the inner surface. Putting one insulating block on the south side (assuming you live in the northern hemisphere) and on the top blocks sides with the strongest incoming sunlight. One on the west side might be a good addition, too, since there is strong solar heating in the evening on the west when the air temperature is the hottest. Probably your box entrance hole faces east to keep rain from blowing in, so insulating the mounting pole side should be easy.
(I’ve been making a living on spacecraft thermal control and atmospheric physics for most of the last 35 years, so I feel confident in making that assessment.)
I’ve heard lots of legends about birds not liking painted houses, but I have not seen it. If they will put up with Carol’s rig they aren’t going to mind a little latex paint. I wouldn’t paint the inside, but my box that is painted on the outside has been a favorite. The only boxes I’ve heard about that need to be colored on the inside hare bat houses. They like things to be black on the inside, so use a water based stain for them, but bird houses should be bare wood.