The transient temperature and stress fields in a hollow cylinder with an axial surface crack subjected to thermal shock are considered. It is found that the temperature boundary effect exists in a thin layer close to the cooled surface, if the nondimensional Fourier number is not very large. For the third kind of boundary condition ( convection boundary condition) due to thermal shock on the inner surface, the asymptotic solutions of temperature fields are deduced for various values of Biot number. The resulting thermal stresses in the uncracked cylinder, which are necessary for the determination of the stress intensity factor, are solved by quasi-static formulation. By introducing the line spring model considering the arbitrary loads on crack surfaces, the numerical results of the stress intensity factors for a semi-elliptical axial surface crack are obtained as a function of Fourier number and the parametric angle of ellipse for various values of Biot number.