This paper studies the thermoelastic fracture in a solid under non-classical Fourier heat conduction. The temperature field and the associated thermal stresses are solved by the dual integral equation technique. Both thermally insulated crack and heated crack are considered. It is found that the crack tip thermal stress is singular and can be expressed in terms of the thermal stress intensity factor in a closed-form. Numerical results show that the crack considerably amplifies the local thermal stresses, confirming the significance of the effect of non-classical heat conduction on the thermoelastic fracture mechanics of materials.