The aim of this paper is the identification of unknown losses in a Permanent-Magnet Synchronous Motor (PMSM) through the thermal assessment of the motor behavior. These unknown losses can be sometimes hardly determined with analytical calculations. Their influence could be critical to some materials of the electric motor, such as windings and rotor, which are sensitive to hot-spot temperatures. The evaluation of the evolution of these unknown losses during cycles of mission is a crucial step in the motor conception phase. The applied method consists in solving a heat transfer inverse problem in real time. A new approach is used in this study for the regularization of the solution. It is based on a past-time averaging method. The work is numerically carried out based on a Lumped-Parameter Thermal Model (LPTM) developed for a high specific-power motor for the propulsion of hybrid aircrafts. Few reachable temperature nodes with known data are considered for the simulation. A dynamical mission profile is studied herein for a flight scenario of a hybrid aircraft, propelled by motors having around 1 MW of power. Three cases are investigated for the losses identification using the inverse technique. A study on the number of past time steps for the regularization of the ill-posed problem is presented. The results show that the thermal heat dissipated due to losses can be accurately estimated with an acceptable average error. The proposed procedure allows real-time determination of losses and monitoring of critical temperatures.