Abstract: A new thermal boundary value problem is investigated. An infinite plate with a central crack is subjected to remotely and uniformly applied heat flow, and there is an angle between the heat flow direction and the crack. When a constant temperature prevails on the crack surface, the analytical solutions of temperature, thermal stress and displacement fields are obtained by using the complex function approach in thermoelasticity. The thermal stress intensity factor is determined from the unique condition of the displacement field. Numerical computation was performed for the aluminum alloy LY12 material. The effects of magnitude and direction of heat flow on the temperature field and thermal stress intensity factor were discussed. The result shows that only mode I thermal stress intensity factor is induced while the mode II thermal intensity factor vanishes under the given thermal boundary condition. Thermal stress field only depends on the component of remote heat flow along the crack direction, while the component of heat flow normal to the crack surface has no influence on the thermal stress field.