We formally describe and verify a real-time temperature control system for a nuclear reactor tank, using a generalization of action systems to hybrid systems (based on weakest precondition predicate transformer semantics) as our formal framework. The analyzed control system is a linear hybrid system, combining discrete control with continuous dynamics. Our work can be seen as a case study on the applicability of the hybrid action system formalism to study the reachability problem, i.e., to prove that an unsafe state can not be reached by executing the system.