how does my thermostat differential work?

I just bought a Johnson Controls A19AAT-2C external thermostat for my chest freezer for my first lager, and I'm trying to figure out where to set the thermostat where the fermentation temperature is supposed to be, say, 40 degrees.

The thermostat has a set differential of 3.5 degrees. Everyone seems to agree that this means it will cool to 36.5 then shut off. My question is when it turns on again. After lots of research, I've noticed that some people think it'll turn on again when the temperature reaches 40, whereas other people, including a poster on this site, https://www.homebrewtalk.com/showthread.php?t=985&highlight=thermostat+differential, say it will turn on at 43.5. I've done a little experimenting with a thermometer, and I think it does the latter, but I'm not sure.

This makes a difference, of course, because if the former is true, the average temperature will be 38.25, whereas if the latter's true, the average temperature will be exactly 40. (Of course, the beer's temperature won't change as much as the air, but that's beside the point since the beer will reach the average temperature, and the 1.75 degree difference in average temperature might be significant over 6 weeks.)

Any thoughts? Thanks in advance.

The difference between 40 & 38.25 is minor. I don't know about the Johnson, but just about every thermostat I've used (be it solar, home, fridge, etc) turns on at the set point and off when the differential is hit. The differential is the entire dead-band, not plus and minus. My Ranco works this way & I verified it with a min-max thermometer.

If you are really concerned about kegger temperatures, you should have a separate thermometer as a check anyway.