Utilizing the excess electric energy from renewables is a crucial step towards reaching climate goals. Synthetic fuels produced via carbon capture and Power-to-X can play a major role in this endeavor. Methanol is a promising synthetic fuel and a base chemical candidate as it can be easily stored and transported in liquid form. Synthetic methanol can be produced via synthesis from hydrogen and carbon dioxide. To study the synthesis process experimentally, we have constructed a bench-scale experimental methanol reactor at Aalto University. In this study we estimate the heat losses in the reactor and elucidate the heat transfer processes between the reactor bed and the process gas flow. We study this by introducing small pulses of process gas to the reactor in a steady nitrogen flow. We vary the size of the pulses and use temperature data collected along the reactor to determine its heat transfer characteristics.