The thermal protection relay determines a value representative of the thermal image of an apparatus to be protected according to a measured current value, to a previous value of the thermal image and to preset heating and cooling time constants. The relay takes into account a non-zero initial thermal image, determined from experimental thermal resistance curves of the apparatus. In the case of a motor, for example, this enables the cold tripping curve of the relay to be lowered without modifying the hot tripping curve, so as to bring the tripping curves of the relay closer to the thermal resistance curves of the motor.