Abstract Seven different thermal regimes can be achieved when an exothermic first-order reaction takes place in a cocurrently cooled fixed-bed reactor. All the regimes are feasible in reactors where the inlet temperature of the coolant is different from that of the reacting stream. New thermal regimes were found; they are qualitatively very different from those commonly reported in the literature (e.g. maximum-minimum, or minimum-maximum profiles, cold-spot regime). Based on a pseudohomogeneous plug-flow model, the conditions of existence for all the regimes, as well as guidelines to select the operating conditions to achieve the desired profile properly are presented. The diversity of feasible regimes can be very useful to track optimum thermal profiles required to solve practical optimization problems.