Networks of catalytic reactors with periodically rotated inlet and outlet ports are studied. A first order irreversible exothermic reaction is considered and the influence of thermal dispersion on the stability limits of periodic regimes corresponding to trains of traveling temperature waves is examined. The dependence of the minimum adiabatic temperature rise sustaining the emergence of temperature wave trains on the enthalpy Peclet number, and on the structure of the spatiotemporal temperature pattern (number of waves and average wave width) is described. The mechanisms determining the evolution of the maximum temperature with the adiabatic temperature rise, the enthalpy Peclet number, the switch time, and the structure of the spatiotemporal temperature pattern are identified. The results provide indications on how to design and operate the network so as to generate temperature wave trains with prescribed structure, maximum temperature and stability limits. (c) 2012 Elsevier Ltd. All rights reserved.