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The computational accuracy of the thermal stress of the internal points by the conventional boundary element methodbecomes more deteriorate when the points approach to the boundary due to the inaccuracy of the calculation of thenearly singular integral by the numerical method.A new natural boundary integral equation for the thermal stress is established by introducing the natural variables,in which the hyper-singular integral is degraded into a strong one and iscalculated by the regularization method.One numerical example is given out to show the present method can efficientlycalculate the stress of the interior point closer to the boundary by comparing with the conventional boundary method.After the stresses of the interior points along the bisector of the V-notch are obtained,the stress method is used tocalculate the thermal stress intensity factors of the V-notch.