An arrangement for preventing overcooking in a combination of cooking utensils with a lid includes an opening mechanism, arranged at the lid, for the regulated manoeuvring of an opening part thereon, which cooperates with an opening in the lid when temperatures close to the boiling point are reached in the cooking utensil. The opening mechanism includes a thermostat with a regulating piston of the type that has a built-in expanding body acting on the piston, the volume of which body is a function of the temperature in the environment of the thermostat. The thermostat is arranged, when temperatures approach the boiling point, to tend to cause the opening mechanism to guide the opening part into an open position in a regulated manner by the regulating piston. A spring is arranged, working against the thermostat to bias the opening mechanism and the opening part to a closed position at the opening.