In a preferred form of an "auto cooking" microwave heating appliance, there are provided two sensors, typically, a gas sensor and a heat-sensible element (i.e. thermistor) within a passageway for outgoing air from a heating chamber. In addition to a switching means for controlling an enabling circuit for a microwave source such as a magnetron, a cook switch is provided which is common to all of the different kinds of foodstuff to be heated. A microcomputer is provided which generates a heating stop instruction for the enabling circuit for the microwave source in response to not only output signals from the heat-sensible element and the gas sensor but also a stored program in the microcomputer. Based upon the rate of timewise variations in the output signal from the gas sensor, the microcomputer decides what kind of foodstuff is being heated and then establishes an intended final level at which the gas sensor shall reach at the end of heating and an intended final level at which the heat-sensible element shall reach at the end of heating. A heating end instruction is issued when both the gas sensor and the heat-sensible element reach their intended final levels.