The self-diffusion of ethane in cation-free Linde type A zeolite has been studied by molecular dynamics simulations for various temperatures. These simulations predict that the diffusivity decreases with increasing temperature between 150 K and 300 K for a low loading of one molecule per cage. The rate of cage-to-cage crossings shows the same temperature dependence. We explain this phenomenon based on an analysis of the activation entropy that controls motion through eight-ring windows separating adjacent cages. The diffusivity and the cage-to-cage rate constant both decrease with temperature because heating the system moves ethane away from eight-ring windows, on average, which increases the entropic barrier for cage-to-cage motion.