The Markovian intensities approach proposed by Gutsche and Hartmann (1995) for predicting the dynamic as well as the steady-state behaviour of chemical reactors is expanded to the non-isothermal case. In comparison with the isothermal case three additional activities are required. The first activity is the derivation of a runaway criterion based on the ratio of the overall Markovian intensity of heat generation to the overall intensity of heat removal. The new criterion is more general than formerly developed ones because it comprises all single mass and heat transport processes occuring within the reactor. Secondly, the intensity ratio is utilized to estimate a characteristic temperature approximating the actual temperature rise in the non-isothermal reactor. This temperature rise is taken in the final activity to predict the dynamic and steady-state behaviour under nonisothermal conditions. A number of simulations demonstrate that the new procedure is applicable to complex non-isothermal catalytic reactors.