<p>In this study, a nonlinear thermomechanical analysis is conducted to explore the dynamic snap-through buckling of circular plates subjected to sudden temperature rises and subsequent impulsive lateral loading. The plate rests on a radially graded nonlinear elastic foundation, modeled as a generalized Winkler-type substrate. The stiffness of this substrate varies with the radius, thereby facilitating precise control over the snap-through response. A closed-form temperature field is first established, followed by the evaluation of the resulting thermal membrane forces and bending moments induced by the rapid heating phase. The transient thermally driven deformation is then computed prior to the application of a mechanical shock load with various spatial distribution functions, which triggers the snap-through instability once the thermal transient stabilizes. Utilizing the Reissner–Mindlin shear deformation theory, the governing dynamic equations are formulated within the framework of axisymmetric kinematics in conjunction with nonlinear strain–displacement relations and uncoupled thermoelasticity. The nonlinear Lagrangian energy functional is formulated, and the dynamic response is obtained through a hybrid numerical–analytical approach that combines a Legendre-polynomial-based Ritz discretization, the Wilson-θ time integration method, and Newton–Raphson linearization for iterative solution of the governing nonlinear system. The snap-through threshold is identified using the Budiansky–Roth criterion, providing refined insights into the instability mechanisms and the role of thermal shock, foundation nonlinearity, and radial stiffness grading on the dynamic stability of thermally loaded structural components.</p>