Can you tell us what country you're in? As @saysfaa indicated, a rocket stove could work. I've even seen them made out of a log. Put whatever you're burning at the bottom of the chamber and adjust the lower entrance towards whatever prevailing wind. They burn very hot and would quickly heat...
I agree with the other posters that, once they've hatched, the quail should be taken away from the bantam and brooded separately.
Without electricity, using a hot water bottle is probably the best way to brood the quail chicks, assuming you can get hot water by some other means.