This paper describes an investigation of various automated control strategies applied to a full-core multiphysics Griffin/Bison/RELAP-7 model of a prototypical nuclear thermal propulsion system. In all cases, control is achieved by actuating control drums based on the demanded power and predicted quantities from the numerical model. One key finding is that hybrid proportional integral derivative controllers – a novel type of controller that uses both power and reactivity predicted signals – can demonstrate a level of performance rivaling that of period-generated control. The former requires parameter tuning, while the latter mostly necessitates providing reactivity coefficients and temperature rates of change, which could be very challenging to accurately measure in real-time.In addition, decay heat plays an important role in determining cooling requirements during cooldown phases. A decay heat model, accounting for burn time and throttling, was derived, and is incorporated within the model to simulate the steady-state and shutdown phases and satisfyingly follow the power demand. However, temperature overshoots and non-constant specific impulse during throttling will necessitate further improvements.