David, It won't take very much heat if you insulate the box at all well. I'd bet a couple 15 or 25 watt light bulbs around the bottom corners with a false bottom of maybe peg board above that to help distribute the heat would do just fine.
You might tear apart an old small electric heater and scrounge the thermostat so it could go just in series with the light bulbs. Since you want a temp of between 85 and 90 degrees that should be in the probable range of such a simple thermostat. I just raise my dough in the gas oven with pilot light and the oven's light on, works fine, but if you have an electric oven it's a pain. BTW, the official name for such a box I think would be a "proofing box" should you want to google that and see if anything usefull comes up. Remember you want the lights not directly shining on the dough or bowls, and there should be room around everything to get some air movement so as to try to keep as even a temp as you can manage. Also, I just tried some King Arthur "white-wheat" flour this weekend, its a different wheat and ground quite fine, so the bread comes out with a texture half way between 100% whole wheat and white. Firm and moist but not so heavy. very good flavor and never gets gooie like white. Hope that helps, maybe others have more comments. Have fun and good breading tom Fowle