The dynamics of a three-catalytic-reactor network, where an exothermic irreversible reaction occurs, is studied. The network is operated by periodically switching feed and discharge positions (with the period being 1). We analyzed the effect of two different switch strategies and observed different spatio-temporal patterns. Such differences result from the different spatio-temporal symmetry that is induced by the switch strategies. Their effect on the stability is studied by comparing the stability range of T-periodic regimes as the switch time is varied for different values of the feed temperature. This analysis is conducted by a numerical continuation technique based on the spatio-temporal symmetry of the forced system. For low (ambient) feed temperature, the stability ranges of a diabatic reactor conform to criteria previously proposed for adiabatic reactors [Sheintuch, M; Nekhamkina, O. AIChE J. 2005, 51, 224]. We observe that these criteria cannot be applied at higher feed temperatures, as a consequence of the external heat losses. One of the examined switch strategies is used to determine a significant widening of the operability conditions.