Another option is a simmerstat, can be liberated from a scrap stove or bought from a spares outlet.Just obtain a rheostat rated higher than 1250W. But rheostats are rarely used in this case anymore, as they don't provide good control. You may want to consider a 2000W dimmer. But even better is a thermostat rated to handle your heating element.
Although it does have the disadvantage of switching the power on and off to control the average power.
The actual thermostat is in the control unit along with its own little heater, turning the dial varies the preload on the bimetal strip to vary the make/break point.