The thermally induced spin‐crossover (SCO) phenomenon in transition metal complexes is an entropy‐driven process, which has been extensively studied through calorimetric methods. Yet, the excess heat capacity associated with the molecular spin‐state switching has never been explored for practical applications. Herein, the thermal damping effect of an SCO film is experimentally assessed by monitoring the transient heating response of SCO‐coated metallic microwires, Joule‐heated by current pulses. A damping of the wire temperature, up to 10%, is evidenced on a time scale of tens of microseconds due to the spin‐state switching of the molecular film. Fast heat‐charging dynamics and negligible fatigability are demonstrated, which, together with the solid‐solid nature of the spin transition, appear as promising features for achieving thermal energy management applications in functional devices.