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One of the most studied catalyst distributions for heat-exchanger reactors is the on–off distribution where fully active and inert regions appear in strategic locations to balance heat transfer between the two reacting streams. In this work, a fundamental study is done, which shows that, given the singular nature of the optimization problem, on–off distributions do indeed make sense, as they correspond to bang–bang type inputs that are observed in singular optimal control problems. In particular, an optimization problem is formulated to find catalyst distributions that maximize conversion, while preventing hotspot formation for heat-exchanger reactors, within the framework of optimal control theory. The optimal control problem turns out to be singular, since the Hamiltonian depends linearly on the control; hence, the optimal profile consists of bang–bang, singular, and constraint arcs. Two different sets of parameters corresponding to quenching and hotspot formation are considered, and it is shown that the optimization results in the intelligent placement of inerts and constraint arcs, consequently increasing the heat transfer efficiency and safety of the reactor in both cases. Piecewise constant approximations of the optimal profiles are obtained and show minimal deviations from the true optimal.