Our luck ran out. The recent cold spell lasted long enough that I had to turn on the electric heater in the coop. The temperatures were in the -20s, with the coldest recorded temperature being -29F.
The fresh air coming in through the pipe that coils inside the biomeiler is still reading 32-37F, but the heat loss of the coop is too great for the interior temperature to stay in the range I like. 45F +/- 10 is my goal for the winter coop temperatures. The coop thermometer was reading 34F on the morning of January 3, and there was a bit of ice in the waterers. So, the temperature was getting too low.
The electric heat in the coop comes from a 600W oil convection heater. The thermostat is set for the 40s and it is on a timer for 50% duty. For safety, the heater is on a shelf on the wall with sheet metal beneath, behind, and above it. The shelf is reasonably high from the floor and too small for a chicken to land next to the heater. The heater is fastened to the shelf and its power cord has been tied short so it will unplug from the socket if the chickens somehow manage to knock it down.
That electric heater, plus the body heat from the chickens has been sufficient to keep the coop warm in the coldest of winters. Chickens at rest produce heat at about 4W/lb. So, my flock gives off about 500W if they are just sitting around and more if they are active.
The cold spell ended after three days. So, we only had to use 14.68 kWh of electricity for heat. The Golden Valley Electrical Association charges us (effectively) $0.31 per kWh, which means it cost us $4.55. Thanks to the biomeiler warming up the air coming into the coop, that is our current total electric heat expense for the winter.
This gives you an A+ for understanding the problem, the scientific mind to address the issue, and energy to earn success in the endeavor.
Reward yourself, as you bask (briefly) in this outcome!