The incubator in the video I described doesn't use a standard thermostat, the aquarium heater is set to the specific temp you want the incubator to be and the heated water provides the temp. Regulation is automatic via the aquarium heater used. I personally recommend the Aqueon Pro series aquarium heaters. They just have a dial to set the temp on the top and you monitor the heat and humidity in the incubator/egg box with an accurite. You definitely want to set it up in advance to allow time to come to temp and adjust as necessary, but once the heater is set and temps are right you shouldn't have to ever adjust again.

I know the concern is whether the aquarium heater will provide the heat needed, but a 50 watt heater can heat 10 gallons of water from 70 degrees to 80 without breaking a sweat, so a 50-100 watt heater heating that little amount of water will definitely work. And since the water in there holds heat so well there should be very little temperature variation from set temp as the water will average the heat input to mitigate hotspots.

Lastly, I know the idea of an incubator without a herpstat is a terrifying idea, but the aquarium heaters need to be able to keep temp very specific in an aquarium setup, and after several years I haven't had an aqueon heater overheat one of my fish tanks. They are incredibly reliable.