The temperature behaviour of transport-reaction systems undergoing single-file diffusion (the particles are not able to change their order) is investigated systematically The influence of exchange limitations at the margins, of attraction between the particles, and of a small possibility that adjacent particles exchange their positions are considered. The investigation is based on an isoline diagram which proves to be a very useful tool applicable to any transport-reaction system. If the channels are crowded, if the intrinsic reaction rate is large enough so that the total conversion is transport-controlled and if the activation energies of the elementary processes of the transport fulfil certain relations (e.g., if passages of neighbouring particles are possible with an activation energy higher than the intrinsic activation energy of the conversion), then the apparent activation energy of the conversion in the single-file system can exceed the intrinsic activation energy. Such a behaviour is impossible for systems undergoing normal diffusion but was found experimentally for some single-file zeolites in the literature.