This work adapts historical literature and existing phenomena identification and ranking tables to be applicable to a novel nuclear power plant (NPP) and chemical or thermal process integrated energy system (IES), particularly focusing on the process heat and heat transport system failure events that are not a concern during normal NPP operation but become vital when an IES is considered. Nuclear energy has been suggested to go beyond baseload applications and be used for hydrogen co-generation systems, among other IESs. Prior to the implementation of nuclear IESs, sufficient analysis must be performed on accident events to ensure public safety. The events considered were deemed important because of their potential to damage systems, structures, and components. Process thermal events of concern include loss of heat load and temperature transient events. Loss of heat load events were characterized as having high importance and being well understood. Temperature transient events may be further categorized by the cyclic loading and harmonics phenomena. Cyclic loading issues were classified as medium to high importance with knowledge gaps existing regarding fatigue and low power operation, while harmonics phenomena were classified as low importance and are well understood. Heat transport system failure events of concern include intermediate and process heat exchanger failures, mass addition to reactor coolant, ingress of material from thermal manifold/energy storage, and loss of intermediate fluid. These events tended to be of high or medium importance, with some knowledge gaps needing to be filled for individual reactor systems due to unique designs.