A cold oil stream is heated in a stirred tank. The dynamic change in temperature in the tank is modelled by an ordinary differential equation, derived via a heat balance The temperature of the liquid in the tank is driven to a set point via a PI controller, which alters the heat added to the system. The optimium controller gains are found by minimising an objective function that describes how far the actual temperature profile is from a user-defined profile. Additionally, overshoot is attenuated via a penalty multiplier to the objective function. This application highlights two Maple computational features - Numeric solution of differential equations - Non-linear optimisation