Parabolic trough solar collectors can be used to drive endothermic reactions, such as methane reforming, while using molten salts as a heat transfer fluid. However, linear focus concentrators can only provide temperatures under 600 °C, resulting in CH4 conversions well below 50%. The equilibrium can be shifted toward much higher conversions if H2 is continuously removed from the reaction mixture via a H2-selective membrane, while simultaneously generating a high-purity H2 stream. In this study, a tube-and-shell, molten salt-heated packed bed membrane reformer (Ni/Al2O3 catalyst, 5 μm supported Pd film membrane) is analyzed numerically using computational fluid dynamics and non-isothermal formulation. The effects of molten salt supply rate and reforming feed flow rate on the reformer performance, which is evaluated in terms of CH4 conversion, H2 recovery, and selectivity to CO, are investigated. Depending on operating parameters, significant temperature and concentration gradients may form in both axial and radial directions. These gradients can be prevented by adjusting feed rates in the reforming and molten salt compartments. For the optimized case, CH4 conversion of 99% and H2 recovery of 87% are predicted for the molten salt feed temperature of 600 °C and reforming feed space velocity of 5000 h−1, which corresponds to a power density of 1.9 kW/L and a fuel heating value upgrade of 40%. A preliminary techno-economic evaluation is provided.