After consulting with the helpful folks at ApplianceParts Pro I ordered a temperature control device (a thermostat).
It was a matter of removing the back panel of the inside of the freezer and then disconnecting 3 wires and the temperature wire. Then the thermostat could be removed. Putting the new one in took a little more effort. The thermostat had changed slightly from the one in my old freezer and I had to use a tin snips to enlarge the opening. After installing the new part, it seemed to work fine until I fastened the back panel the that part was on. It stopped working. After some more fiddling and much prayer, the Lord started it up!
It now seems to be working fine.