This paper deals with a mathematical model of a non‐isothermal chemical reaction described by nonlinear ordinary differential equations with two‐dimensional control. The control variables correspond to the possibility of manipulating the concentration of the input reactant and the total flow rate. We consider the task of maximizing the reactor performance as an isoperimetric optimal control problem with periodic boundary conditions. Necessary optimality conditions are derived by the Pontryagin maximum principle with Lagrange multipliers corresponding to the isoperimetric constraints.