Induction heating method implemented in a device for heating a metal part, the device including magnetically coupled inductors (Indl, Ind2,..., Indp), each inductor being powered by a dedicated inverter (O1, O2,..., Op) associated with a capacitor (C1, C2,..., Cp) such as to form an oscillating circuit (OC1, OC2,..., OCp), said oscillating circuits having at least approximately the same resonance frequency, each inverter being controlled by a control unit (M1, M2,..., Mp) such as to vary the amplitude (A 1, A 2,..., Ap) and the phase (φ 1, φ 2,..., φ p) of the current (I 1, I 2,..., I p) passing through the corresponding inductor, the device also including means for determining said current (I 1, I 2,..., I p) as well as means for determining an actual temperature profile (θ 1 mes, θ 2 mes,..., θ n mes) of said metal part, said method including the following steps: a) comparing said actual temperature profile (θ 1 mes, θ 2 mes,..., θ n mes) with a reference temperature profile (θ 1 ref, θ 2 ref,..., θ n ref) and calculating a profile of the reference power density (Dp ref 1, Dp ref 2,..., Dp ref n) which the heating device must inject into said part in order to achieve said reference temperature profile; b) from a matrix of impedances determined by knowledge of the electromagnetic relationships linking said inductors with each other and with said part and by knowledge of vector image functions ( f k) representing the relationships between the current densities created by the inductors and the currents (I 1, I 2,..., I p) passing through the inductors, calculating the target currents which the inverters must produce in order for the currents of the inductors to reach target values (I 1 ref, I 2 ref,..., I p ref) that are suitable for injecting said reference power density profile (Dp ref 1, Dp ref 2,..., Dp ref n,) into said part; c) determining the currents (I 1 mes, I 2 mes,..., I p mes) passing through the inductors in order to compare them with said target values (I 1 ref, I 2 ref,..., I p ref) and to determine current deviations (θI 1 corr, δI 2 corr,..., δI p corr) to be corrected, and sending correction instructions to said control units (M1, M2,..., Mp) in accordance with said current deviations in order to control the inverters such as to correct the currents passing through the inductors. a) comparing said actual temperature profile (θ 1 mes, θ 2 mes,..., θ n mes) with a reference temperature profile (θ 1 ref, θ 2 ref,..., θ n ref) and calculating a profile of the reference power density (Dp ref 1, Dp ref 2,..., Dp ref n) which the heating device must inject into said part in order to achieve said reference temperature profile; b) from a matrix of impedances determined by knowledge of the electromagnetic relationships linking said inductors with each other and with said part and by knowledge of vector image functions ( f k) representing the relationships between the current densities created by the inductors and the currents (I 1, I 2,..., I p) passing through the inductors, calculating the target currents which the inverters must produce in order for the currents of the inductors to reach target values (I 1 ref, I 2 ref,..., I p ref) that are suitable for injecting said reference power density profile (Dp ref 1, Dp ref 2,..., Dp ref n,) into said part; c) determining the currents (I 1 mes, I 2 mes,..., I p mes) passing through the inductors in order to compare them with said target values (I 1 ref, I 2 ref,..., I p ref) and to determine current deviations (θI 1 corr, δI 2 corr,..., δI p corr) to be corrected, and sending correction instructions to said control units (M1, M2,..., Mp) in accordance with said current deviations in order to control the inverters such as to correct the currents passing through the inductors.