Piezoelectric shunt damping offers a passive solution to mitigate mechanical vibrations: the electromechani-cal coupling induced by piezoelectric patches bound to the vibrating structure allows the transfer of vibration energy to an electrical circuit, where it can be dissipated in a resistive component. Among the existing passive piezoelectric shunt circuits, the resonant shunt leads to significant vibration damping if it is tuned with enough precision. However, temperature may have a strong influence on electrical parameters such as the piezoelectric capacitance and the circuit inductance. As a consequence, a temperature variation can lead to a deterioration of vibration damping performance. This paper describes how inductive components can be chosen to minimize the mistuning of the resonant shunt when temperature evolves. More specifically, inductors are made of magnetic cores whose magnetic permeability varies with temperature, which counterbalances the variations with temperature of the mechanical resonance frequency and of the piezoelectric capacitance. Experiments show the benefits of adequately choosing the magnetic material of the inductor for vibration damping of a cantilever beam. The concept of a fully passive shunt adapting to temperature variations is hence validated.