Estimates are derived for the maximum bed temperature in a reverse-flow reactor in which two reactions, having relatively low adiabatic temperature rise, occur and are mass-transfer limited at the high temperature zone in the bed. The estimates are derived using a pseudohomogeneous model and a step-approximation of the temperature dependence of the observed rate expression. When the switching frequency is very high, the estimate of the bed temperature is given by eq. (16). When the switching frequency is very low, the reactions may be completed either in a temperature front moving at a constant velocity and shape, or in two consecutive temperature fronts, separated by an almost constant temperature plateau, with the upper front moving faster than the lower one. The corresponding maximum bed temperature for these two cases is given by eqs (29) and (38), respectively. A simple criterion predicts which of the two types of front movement occurs. The estimates show that for reactants with low adiabatic temperature rise, the maximum bed temperature depends mainly on the critical temperature of the reactions, defined by eq. (8), and only weakly on the switching frequency. When the two critical temperatures are widely separated and both reactants are converted in the reactor, the maximum bed temperature is essentially independent of the reaction occurring at the lower temperature.