The thermal transient load of the primary loop nuclear pipeline will cause fatigue damage at sensitive locations.And cumulative fatigue damage factors of these sensitive locations need to be monitored during the life extension of the nuclear power plant,and thermal transient stresses need to be calculated rapidly during online monitoring. Taking the thermal shock of the spray nozzle of pressurizer as an example,the double temperature boundary Green’s function method is discussed. By the volume integration of Green’s function,the transient thermal stress under the heat-up condition is calculated. The accuracy of the two temperature boundary Green’s function is verified by comparing with the direct calculation results of finite element method.Studies have shown that the Green’s function should be established separately for subdivisions which are divided according to the differences of the flow heat transfer boundary（ such as the convection heat transfer coefficient） and the width of the temperature range. While in a certain temperature range,it is feasible to establish the Green’s function based on the average temperature of the temperature range with large enough step temperature.