A method including: a) determining a value representative of temperature of exhaust gases flowing in an exhaust duct of an engine upstream from a turbine; b) comparing the representative value with a predetermined threshold value; c) if the representative value is higher than the threshold value, initiating timing-out of a first time delay during which a) and b) are repeated; d) if the representative value is lower than the threshold value, initiating the timing-out of a second time delay during which a) and b) are repeated; e) if the first time delay has elapsed and the representative value is higher than the threshold value, preventing the automatic stoppage of the engine; f) if the second time delay has elapsed and the representative value is lower than the threshold value, authorizing the automatic stoppage of the engine and resetting the measure of the timing-out of the first time delay.