Thanks for the very clear response! I emptied out the freezer and took a look around. When I realized I wasn't sure what was what, I went to the
RepairClinic.com site that I saw mentioned elsewhere and looked at the pictures; it really helped.
The thermostat read >10kohm (as high as my meter goes) with frosty ice on it, so that's probably it?
I disconnected the heater element and stuck the meter across it and measured 6 ohms. According to the component specifications that I found under the fridge, the "evaporator heater" (same thing?) is supposed to read 29 ohms, plus or minus 5%. Is this also a problem?
I don't think it's a clogged defrost line. When I defrosted the fridge last week, there was a nice little puddle under the fridge, despite the (mostly dry) towels I had inside the freezer.
I've also attached a picture, in case it helps.
So, what's my next move?