I've used a cartridge heater, but in DC voltage. Typically the type used in 3D printers. As a power source, I re-use a laptop computer charger/convertor. Both the heater and the charger are 24vdc. If needed, the charger may be plugged into my PID.
Best thing is the heaters are only $10 for 5 of them. Computer charger was a salvage from work and the PID was already built.
The cartridge heater is inserted into a 1" thick aluminum plate, which is under the lube sizer.