Hydrogen is considered as an alternative to fossil fuels for energy production due to its high energy density and zero carbon emissions. It is typically produced from hydrocarbons via steam reforming or the water gas shift (WGS) reaction. In this paper, we develop a distributed model for a WGS membrane reactor which achieves higher carbon monoxide conversions than these achieved by conventional packed bed reactors. A steady-state analysis under different flow configurations reveals the presence of large temperature gradients (hot spots) in the reactor. Open-loop simulations demonstrate the necessity for a control strategy to suppress the hot spot and maintain the operation of the reactor under a specified temperature reflecting a catalyst operating limitation. Three different control strategies are proposed and a case study illustrates and evaluates their performance. A comparative study between a nonlinear and a PI controller is also performed.