A great deal of research in the chemical engineering literature on steady-state multiplicity analysis, nonlinear dynamics, and chemical process control has been based on the (now) classic two-state continuous stirred tank reactor (CSTR) model. One assumption of this model is that the cooling jacket temperature dynamics are negligible, hence the cooling jacket temperature is the manipulated input for feedback control of reactor temperature. However, since the dynamics of the jacket and reactor are nonlinearly related via energy transfer through the reactor wall this is not in general a very good assumption. The influence of process design parameters on the open-loop behavior of a three-state CSTR model (which incorporates an energy balance around the cooling jacket) is considered in this work. The effect of cooling jacket feed temperature on isola behavior is studied. We show that infeasible reactor operation regions may occur when the reactor is "scaled up"; process operation changes are recommended to move reactor operation back into a feasible region. A multiple time-scale perturbation analysis is used to understand the effect of cooling jacket size on the oscillation amplitude of the three-state CSTR model at a Hopf bifurcation point.