In this paper, the fracture problem of a functionally graded piezoelectric material strip (FGPM strip) containing an infinite row of parallel cracks perpendicular to the interface between an FGPM strip and a homogeneous layer is considered. The problem is solved for the laminate that is suddenly heated from the surface of the FGPM strip. The surface of the homogeneous layer is maintained at the initial temperature. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. By using the Fourier transform, the thermos-electro-mechanical fracture problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time for the various values of the nonhomogeneous and geometric parameters. The results for the crack contact problem are also included.