It started popping every so often like a light bulb flaming out. No visible arc or sparks, just an annoying noise at first. Then it got more frequent and louder and then the ice cream got soft. Seemed to be struggling, compressor switching on and off too often. Diagnosis gave me a good excuse to vacuum all the cat hair out of the coils. Changing out the thermal cutout was as easy as changing a light bulb, if you don't count having to crawl in the dark and dust to remove the access panel behind the fridge. Replaced the indicated items and now the ice cream is properly frozen again and all weird noise has stopped. Hooray for The Internet!!