Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches subjected to different sudden thermal loads are studied. Temperature and position dependence of the material properties are taken into account. Based on the uncoupled thermoelasticity assumptions, The non-linear one-dimensional transient heat conduction equation is solved numerically by a hybrid iterative GDQ method and Crank-Nicolson time marching scheme. A first order shear deformation arch theory (FSDT) is also combined with the von Kármán type of geometrical non-linearity and the Donnell kinematic assumption to obtain the equations of motion employing the Hamilton principle. Discretization of the highly coupled non-linear equations of motion is done by using the GDQ method in the arch domain. The solution of the system of the ordinary differential equations is established by means of a hybrid iterative Picard-Newmark scheme. Comparison is also made with the existing results for the case of isotropic homogeneous shallow arches, where good agreement is obtained. Also, parametric studies are proposed to show the effects of temperature dependency, geometrical non-linearity, arch thickness, power law index, and the type of thermal-mechanical boundary conditions upon the arch deflection.