The dynamic behaviour of a tubular reactor with axial diffusion and a countercurrent coolant is simulated by means of the so-called straight-line method, together with a semi-implicit Runge-Kutta scheme. The present paper is focused on the analysis of the peculiar type III intermittency transition to chaos exhibited by a tubular reactor for a proper set of parameters values : suitable methods of numerical and statistical type are considered in order to characterize in detail the phenomenon at hand and to recognize it from the theory. As far as we know, this is the first example, among a few ones reported in literature, in chemical engineering.