The fact that a microwave oven uses a magnetron, and a magnetron is a type of valve - reducing the mains to the oven reduces the heater voltage, preventing the magnetron from oscillating. A common fault in microwaves is poor crimping on the push-on terminals for the magnetron heater, and the small loss of voltage caused by the 'high' resistance (a fraction of an ohm) prevents the magnetron oscillating reliably.
The first thing you do when repairing a 'not heating up' microwave (after discharging the HV capacitor!!!) is remove the terminals, give the tag crimps two or three squeezes with a pair of side cutters, and then solder them as well. Then you see if it now works, quite often it does, and if not you start fault finding properly.