This paper studies the fracture mechanics of a piezoelectric material layer with an internal crack under the framework of hyperbolic, non-Fourier heat conduction. The paper includes two parts. The first part is for the case of a heated crack, in which the internal crack can be a source of heating (or cooling). This case develops the mode I thermal stress intensity factor at the crack tip. The second part is for the thermally insulated crack, which does not allow any penetration of the thermal flow across the crack. This case develops the mode II thermal stress intensity factor at the crack tip. Numerical results for the thermal stress intensity factor are plotted to show the effects of the thermal relaxation time, the crack length and the layer thickness. Comparisons between the non-Fourier results and the classical Fourier results are made. Limiting cases of the current problem include the solutions of thermoelastic crack problem and fracture mechanics associated with classical Fourier heat conduction.