A method of determining internal temperatures in a synchronous electric machine, said synchronous electric machine comprising a stator consisting of three phases on each one of which at least one coil is connected, and a rotor comprising at least one magnet, the electromagnetic field of said coils causing rotation of said rotor, a method wherein speed Ω m of said rotor, as well as voltages and currents u m and i m of said phases are measured, characterized in that the following stages are carried out: a) estimating a resistance R̂ for said coils by means of a state observer of the resistance R̂ of the coils from said measurements, said resistance depending on the temperature T cu of said coils, b) estimating an intensity of the magnetic flux φ̂ of said magnet by means of a state observer for the intensity φ̂ of the magnetic flux of the magnet from said measurements, said magnetic flux intensity depending on the temperature T ai of the magnet, c) determining voltages u d,q and currents i d,q in Park's reference frame through transformation of the measured voltages u m and currents i m, d) designing an observer which calculates, in real time, an estimation ( î d, î q) of the currents ( i d, i q) of the type as follows: L d i ^ ̇ d = − R ^ T cu i ^ d + p Ω m L q i ^ q + u d − k d i d − i ^ d L q i ^ ̇ q = − R ^ T cu i ^ q − p Ω m L d i ^ d + φ ^ T ai + u q − k p i d − i ^ d; where R̂ and φ̂ are estimations of the resistance of the windings and of the flux of the magnet and L d: direct inductance of said electric machine, L q: quadrature inductance of said electric machine, k d, k p: calibration variables, p: number of pole pairs of the electric machine, e) determining a temperature T cu for said coils by means of said estimation of resistance R̂ of the coils, said resistance R̂ being estimated by means of said estimated currents î d and î q, and f) determining a temperature T ai for said magnet by means of said estimation of the intensity of magnetic flux φ̂ of the magnet, said magnet flux φ̂ being estimated by means of said estimated currents î d and î q. a) estimating a resistance R̂ for said coils by means of a state observer of the resistance R̂ of the coils from said measurements, said resistance depending on the temperature T cu of said coils, b) estimating an intensity of the magnetic flux φ̂ of said magnet by means of a state observer for the intensity φ̂ of the magnetic flux of the magnet from said measurements, said magnetic flux intensity depending on the temperature T ai of the magnet, c) determining voltages u d,q and currents i d,q in Park's reference frame through transformation of the measured voltages u m and currents i m, d) designing an observer which calculates, in real time, an estimation ( î d, î q) of the currents ( i d, i q) of the type as follows: L d i ^ ̇ d = − R ^ T cu i ^ d + p Ω m L q i ^ q + u d − k d i d − i ^ d L q i ^ ̇ q = − R ^ T cu i ^ q − p Ω m L d i ^ d + φ ^ T ai + u q − k p i d − i ^ d; where R̂ and φ̂ are estimations of the resistance of the windings and of the flux of the magnet and L d: direct inductance of said electric machine, L q: quadrature inductance of said electric machine, k d, k p: calibration variables, p: number of pole pairs of the electric machine, where R̂ and φ̂ are estimations of the resistance of the windings and of the flux of the magnet and L d: direct inductance of said electric machine, L q: quadrature inductance of said electric machine, k d, k p: calibration variables, p: number of pole pairs of the electric machine, e) determining a temperature T cu for said coils by means of said estimation of resistance R̂ of the coils, said resistance R̂ being estimated by means of said estimated currents î d and î q, and f) determining a temperature T ai for said magnet by means of said estimation of the intensity of magnetic flux φ̂ of the magnet, said magnet flux φ̂ being estimated by means of said estimated currents î d and î q.