Several recent papers have demonstrated that charge-carrier mobility in organic field-effect transistors made of vacuum-evaporated films may become temperature-independent at low temperature. To account for this behavior, we developed a model 1 based on the polycrystalline nature of these films, where charge transport is mostly limited by grain boundaries. The free-carrier density in the intergrain regions is controlled by traps, which leads to the formation of back-to-back Schottky barriers at each side of the grain boundaries. The height and width of these barriers is estimated from solving Poisson's equation using the graded-channel approximation. It is shown that in most cases the barrier width is negligibly small as compared to the physical size of the grain boundaries. In the high-temperature regime, the conducting channel can be simply described by grains and grain boundaries connected in series, so that the overall resistance reduces to that of the grain boundaries. At low temperatures, tunneling through the barrier becomes predominant, leading to temperature-independent mobility. A complete two-dimensional model for charge tunneling through the barriers is developed. A quantitative check of the model is made by least-squares fitting of the gate voltage-dependent current measured on an octithiophene transistor at low temperature, which gives a reasonable determination of the trap density and size of the grain boundaries.