For the first time, a thermal study and optimization of a thermally driven hydrogen compressor has been performed. Experiments on this compressor, which is a proof of concept we developed, are time-consuming, making it difficult to know the behavior of the compressor under a variety of possible thermal conditions. In order to understand its behavior, we developed a numerical model to study the evolution of hydrogen pressure, flow rate, and temperature when heat transfers are intensified by changing the heating power, the setpoint temperature, or the convective regime. Hydrogen compression and discharge were simulated by finite elements and the tank was modeled by an axisymmetric 2D geometry. The heat and mass conservation equations for hydrogen were solved and the predictions were validated by using three heating powers during desorption: 100W, 200W and 300W. A parametric numerical study on the effect of heating power and final set temperature showed that the higher the power, the more hydrogen is discharged, and that the amount of hydrogen discharged varies quasi-linearly with the final set temperature, as long as it is below 500K. Finally, we have shown that increasing the heat transfer by convection with the outside air reduces the time to reach the room temperature by approximately 75%.