Some thoughts, based on building an energy efficient house that uses a wood stove for heat. Temps fluctuate in the house, but is moderated by heavy insulation.
1. Use a well insulated housing, like a cooler.
2. Ditto on heat sinks like rocks or bricks. We use this theory as a large brick wall and pad that the wood stove sits on. It heats up when the stove is burning during the night and lets of heat when the stove is closed down for the night.
3. Mobility--using sunlight thru a window to supplement and move it around. Maybe someone can chime in on moving eggs around like this. If the eggs are turned regularly, pwrhaps moving the whole set up would be OK.
4. DOes a still air system loose less heat? I would think it would. Though the moving air keep a more constant heat through out the incubator. Control the air loss (heat loss), not eliminate it, reduce it to a reasonable level.
5. We use our dogs on very cold nights to sleep with us. Big bodies put out a lot of heat--we joke about 2 dog nights, a 4 dog night, etc.
My point, can you put dogs or other large body in a small room overnight to reduce heat loss over night when the temperatures are dropping in the house. 5-7 am is the coldest time in our house.
6. Size is important too. THe larger the incubator, the more heat sinks possible therefore more less fluctuation. Too big is a problem, too; it'a a balancing act.
THese are ideas as food for thought; maybe they will prompt other ideas as well.
I'd love to be off the grid too!