Present study deals with the dynamic snap-through phenomenon of an isotropic shallow spherical cap under transient type of thermal loading. The inner surface of the shell is subjected to sudden temperature elevation, whereas the outer surface is kept at reference temperature. Transient thermal shock is applied uniformly and shell thickness is assumed to be thin enough. Therefore, transient heat conduction equation is analytically solved across the thickness direction (one dimensional). Immovable simply-supported boundary conditions are assumed for the shell. Since the boundary conditions and the applied thermal shock are axisymmetric, the governing motion equations of the shell are restricted to the case of axisymmetric. First order shear deformation theory of shells is utilized to approximate the displacement field. The von Kármán type of geometrical non-linearity is used in strain-displacement relations. With the establishment of the associated Hamilton principle, differential equations of motion are extracted. Motion equations are discretized within the shell domain by means of the harmonic differential quadrature method (HDQM). The Newmark time marching scheme based on the constant average acceleration method is applied to turn the motion differential equations into a system of algebraic equations at each time step. Highly coupled equations are solved implementing the well-known Newton-Raphson iterative technique. By means of the Budiansky criterion, critical thermal shock parameters are distinguished. Critical dynamic snap-through temperatures are also verified using the phase-plane presentation. Comparison study is performed to validate the formulation and solution method of the present research with simple cases. Also, parametric investigations are performed to demonstrate the geometrical effects on the dynamic critical buckling temperatures of the shallow spherical shells subjected to thermal shock. •Symmetric, nonlinear coupled motion equations of spherical shell under thermal shock are solved.•Dynamic snap-through phenomenon is investigated for shallow spherical shells.•Budiansky criterion and phase plane approaches are used to detect the critical dynamic buckling temperatures.•The importance of inertia effects which results in thermally induced vibration phenomenon is highlighted.