The piezoelectric resonant shunt is an electromechanical device that can significantly damp mechanical vibrations if it is finely tuned. However, temperature may influence the electrical components of the shunt and the mechanical parameters of the vibrating structure, and deteriorate the damping performance as a consequence. The objective of this work is to describe how inductive and capacitive components can be chosen so that the shunt tuning is maintained in the case of temperature variations. Two solutions of fully passive adaptive shunts are developed, tested and compared. The first solution includes a variable inductance. In contrast, the second solution includes a variable capacitance and intends on keeping the shunt inductance as constant as possible. Experiments validate the concept of a resonant shunt that autonomously adapts to temperature variations.