We investigate proton transport in a polymer electrolyte membrane using continuum theory and molecular dynamics (MD) computer simulations. Specifically our goal is to understand the possible molecular origin of the effect of water content on the activation energy (AE) and pre-exponential factor of proton conductivity, in comparison with experimental observations reported for Nafion, where a decrease of AE with increasing water content has been observed. We study proton diffusion in a single pore, using a slab-like model. We find that although the average proton diffusion coefficient is several times smaller in a narrow pore than in a wide water-rich pore, its AE is almost unaffected by the pore width. This contradicts an earlier proposed conjecture that the sizable Coulomb potential energy barriers near the lattice of immobile point-like SO3– groups increase the AE in a narrow pore. Here we show that these barriers become smeared out by thermal motion of SO3– groups and by the spatial charge distribution over their atoms. This effect strongly diminishes the variation of the AE with pore width, which is also found in MD simulations. The pre-exponential factor for the diffusion process, however, decreases, indicating a limited number of pathways for proton transfer and the freezing out of degrees of freedom that contribute to the effective frequency of transfer. Decreasing the pore size diminishes bulk-like water regions in the pore, with only less mobile surface water molecules remaining. This hampers proton transfer. The increase of AE takes place only if the thermal motion of the SO3– head groups freezes out simultaneously with decreasing water content, but the effect is not profound. The stronger effect observed experimentally may thus be associated with some other rate-determining consecutive process, concerned with polymer dynamics, such as opening and closing of connections (bridges) between aqueous domains in the membrane under low water content.