The accurate prediction of the response of aircraft panels subjected to strong acoustic excitation and high temperatures has been and remains an important requirement for the design of supersonic/hypersonic vehicles. One of the key challenges to achieving this prediction is the computationally efficient modeling of the complex physical processes taking place when the acoustic excitation is strong enough to induce a large, nonlinear geometric response of the panel. Even for a flat beam or plate, there exists a subtle energy exchange between the large transverse displacements resulting directly from the acoustic excitation and the much smaller in-plane motions nonlinearly induced by the change of geometry. The transverse displacements exhibit a stiffening behavior which is softened by the in-plane motions. Curved and buckled panels exhibit an even more complex behavior as they can "snap" through an unstable region leading to deformations that are drastically nonlinear, i.e. of the order of 10-100 thicknesses. The interplay of the curvature, acoustic excitation, and temperature leads to an occurrence of snap-through events varying from very rare, to frequent, to continuous. The present study demonstrates that reduced-order model can capture the complex snap-through behavior of shallow curved beams. Successful displacement comparisons are made for two different reduced-order modeling methods, for a single curved beam geometry considering combinations of thermal effects and loading.