We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the organising centre is a pitchfork singularity for both the adiabatic and diabatic reactors. However, unlike the adiabatic reactor, Hopf bifurcations may occur in the diabatic reactor. We construct the degenerate Hopf bifurcation curve by determining the double-Hopf locus. When the steady-state and degenerate Hopf bifurcation diagrams are combined it is found that there are 23 generic steady-state diagrams over the parameter region of interest. The implications of these structures from the perspective of flammability in the CSTR are discussed.