That thermometer has now been displaced into our new freezer. From which we learn that the chesty deep-freeze compartment is currently around -10°F, while the drawer beneath is somewhere between 15 and 20°F.
Which hands me a delicate little quandary, if true: because the deep-freeze section could very easily be kept ten degrees warmer than that, while the drawer section really wants to be cooler. And there is only one thermostat control.
According to the internets, there should be a fifteen-to-twenty degree difference between the two, rather than the twenty-five-to-thirty that we are currently seeing.
It is possible that the thermometer is simply not accurate or consistent. We need more testing; I'm going to turn up the thermostat and see what happens, in both sections. And think again about buying a new thermometer.
Science: it just gets everywhere, y'know?