PURPOSE: To suppress a temperature rise of a part to be easily brought into contact with a predetermined part of each functional section, i.e., a thermally weak part or a hand by allowing heat generating parts to be individually set to heat generating states in a composite cooking implement.

CONSTITUTION: The composite cooking implement comprises a capacity adder/ subtracter 4 for adding a numeric value corresponding to a heat generating quantity of a heat generating part each time the generating part is started to be used and subtracting the numeric value corresponding to the heat generating quantity of the generating part each time the use of the generating part is stopped. A heat generation limiter 5 for limiting the use of an unused heat generating part when an output of the adder/subtracter 4 coincides with a set value H0 lower by a predetermined value than a numeric value corresponding to a total heat generating quantity of the entire implement, is provided.