In this paper, the response of a piezoelectric actuator consisting of a functionally graded piezoelectric material strip (FGPM strip) with a penny-shaped crack and a homogeneous layer induced by a transient thermal load is considered. It is assumed that the thermo-electro-elastic properties of the FGPM strip vary continuously along the thickness of the strip, and that the crack faces are thermally insulated and electrically impermeable. By using both the Laplace and Hankel transforms, the thermal and electro-mechanical problems are reduced to a singular integral equation and a system of singular integral equations, which are solved numerically. Numerical calculations are carried out, and the detailed results are presented to illustrate the influence of the geometric parameters and the material non-homogeneity on the intensity factors vs. time.