I have done it with a custom circuit made of a single comparator, MOSFET and some resistors soldered to a SOIC breakout board. It sorta worked.
Things to watch out for:
A1321 type heater (with ceramic heating element and thermistor rather than thermocouple) is piezoelectric, sharp voltage steps will cause it to "tick" audibly when it turns on/off. Can be annoying and perhaps harmful to the heater
Not a problem with the A1322 and A1323 parts with thermocouples and nichrome wire heaters.
At turn-off, inductance of the cables will cause voltage spikes at the transistor. Add a freewheeling diode or observe RBSOA, avalanche ratings etc of the transistor.
The sharp turn-on and turn-off transients will couple capacitively and inductively into the ground wire. There will be voltage across the wire itself and even if its end is tied to ground you will see voltage spikes at the soldering tip. Possibly a problem for sensitive low voltage CMOS parts.
I reduced them a bit by adding a gate resistor at the MOSFET and hence slowing down the output edges. Perhaps a better solution is to add a choke in series with the heater and a freewheeling diode covering the whole heater-choke circuit.