running phase the shutdown of engines just after the end of the flight requires precautions in terms of procedure since the engine thermomechanical condition is still high at this time this indicator can have any number of conditions depending on the accuracy of the processings implemented in the embodiment being described hereinafter in reference to fig2 the means 5 compare the current value etc determined by the means 3 of the thermomechanical condition et to two different threshold values s 1 and s 2 and the indications being displayed depend on the result of all these comparisons in this case the turbine engine can have one of the three following thermo mechanical conditions p 1 p 2 and p 3 high p 1 when the current value etc is higher than or equal to the biggest threshold value s 1 intermediate p 2 when the current value etc is between the two threshold values s 1 and s 2 and low p 3 when the current value etc is lower than or equal to the lowest threshold value s 2 when the means 5 infer that the thermo mechanical condition of the turbine is high the indication l 1 being showed on the viewing screen 9 indicates as a text in particular as an abstract and or as symbols that the turbine engine shutdown being monitored is to be avoided if possible such a shutdown actually exposes to a risk of turbine mechanical lock.