The problem of controlling a (possibly open-loop unstable) continuous exothermic reactor with temperature measurements and manipulation of reactant feed and heat exchange rates is addressed within a passivity-dissipativity framework. The combination of a nonlinear passive state-feedback (SF) controller with a dissipative observer yields the dissipative output-feedback(OF) controller closed-loop stability conditions with: (i) the identification of the underlying gain-behavior interplay, and (ii) simple tuning guidelines. The approach is tested through numerical simulations, with a representative worst-case example: an exothermic reactor with Langmuir-Hinshelwood nonmonotonic kinetics, which must be regulated about an open-loop unstable steady-state which is not observable.