The telescoping lid I made has a 2.5 inch pine rim, and inside it under 3/8 exterior ply primed & painted...is 1 inch R5 insulation board.
The inner lid with bee space-side down and 1/8" mesh over the escape stops the bees from chewing the insulation. The mesh makes top on the inner lid into yet another SHB jail. SHB are pushed out of the top of the hive body and stay between the inner lid and telescoping lid. Where, I hope, they starve in hopes of sneaking back in. Usually I smash them when I open the top.
I have the $11 sheet metal lid cover from Dadant nailed to the top of the telescoping lid. This is what I was wondering about painting to keep the hive cooler.
And yes I have a top entrance for heat vent, as well as a reduced bottom entrance when the hive is big enough. The bees all prefer the top entrances. They will festoon on the top in the evening, instead of bearding on the front. Even though I know there's plenty of room in the hive.