The occurrence of combustion instabilities in high-performance engines such as gas turbines is often affected by the thermal state of the engine. For example, strong bursts of pressure fluctuations may occur at cold start for operating conditions that are stable once the engine reaches thermal equilibrium. This observation raises the question of the influence of material temperature on the response of flames to acoustic perturbations. In this study, we assess the influence of the temperature of the flame holder for a laminar flame. Both experiments and numerical simulations show that the Flame Transfer Function (FTF) is strongly affected by the flame-holder temperature. The key factors driving the evolution of the FTF are the flame-root location as well as the modification of the flow, which affects its stability. In the case of the cooled flame-holder, the formation of a recirculation zone is identified as the main impact on the FTF