A method of characterizing a turbine engine, the method comprising: steps of using measurements from an accelerometer monitoring a particular turbine engine while it is starting to detect the energy released by any contact during said starting between the rotor and the stator of the turbine engine, and of associating any such detection of contact with thermodynamic data measured on the particular turbine engine; and then a recognition training step, based on the associations, to enable a thermal context of the turbine engine to be used to recognize the presence of a rotor thermal unbalance to be taken into account in order to avoid contacts between the rotor and the stator on starting.