Sounds like the thermostat contacts stuck closed. Most I've seen shut off at 45°F or near that. I have landscaping rocks around mine and filled that with pea gravel.
JT
How this kind of thing happens is a device with wires that can't carry the common 20 amp circuit breaker will burn instead of tripping the breaker. Before we have to see the giant GFCI photo again this is a good information on how they work...