It's hard to imagine the heating element itself being bad, there are no moving parts and it's a simple design. So, I would check to make sure the plug connector is firmly seated on the block heater itself. A PITA because of it's location, but if it's on, then you may have a plug with a bad thermostat in it.
If it is the blister kind of plug, then cut off the round part of the blister, pull out the little round, thin metallic thermostat and stick a small metal washer or a dime in there, make sure it is tight, put the rubber blister back on and tape it back together tight. Make sure the washer is making contact all the time. That will eliminate the thermostat in the plug and you should get current to the block heater regardless of temp.
Just use caution when cutting the blister, at those temperatures, that rubber is like hard plastic and difficult to cut. I first tried using a utility knife but that was useless, I wound up using a Dremel tool and that worked sweet. Good luck. BTDT.
DEWFPO