Great progress has been made in the last two decades on the construction of non-intrusive reduced order models (ROMs) for the prediction of the response of structures with nonlinear geometric effects subjected to mechanical loading. Nevertheless, some challenges remain when the technique is extended to coupled structural-thermal problems. One such challenge is the construction of basis functions to account for the thermal effects on the structural deformations, especially when the temperature field is local and varies with time. The basis construction considered here starts with the basis relevant to the structure without temperature effects and then adds “enrichment modes” that capture the specificities of the thermal response. A systematic analysis of such possible enrichments and their potential benefits was recently performed (Wang and Mignolet, Proceedings of the 38th IMAC, conference and exposition on structural dynamics, Houston, TX, 2020). In the present study, the curved panel studied in that investigation is considered again but the optimal enrichment strategy established there is extended to a two-temperature-field local heating scenario, heating near the quarter of the panel in one case and near its middle in the second. The established enrichment strategy is firstly used to construct the enriched structural basis that captures the response of the panel under any linear combination of the two temperature fields which serve as two thermal modes. Two approaches are then followed to reduce the number of nonlinear enrichment modes and construct compact ROM bases. The first approach invokes the recently developed “progressive POD” method which was originally used for the reduction of the CFD data stored in multidimensional arrays (Wang et al., J. Aircr., 56:2248–2259, 2019). A notable reduction in the size of the basis is observed with this method. The second approach is using the static condensation to incorporate the in-plane components of the enrichment modes. The three ROMs constructed were found to lead to predictions of the structural responses that closely matched their counterparts determined from the underlying full finite element model.