The boundary element method (BEM) does not require a domain integral in steady thermoelastic problems without heat generation. However, in problems with heat generation, the domain integral is necessary. This article shows that the axisymmetric problem of steady thermoelasticity with nonuniform heat generation over the region can be easily solved without a domain integral by means of BEM. This method can also be applied to steady thermal stress problems under complicated general heat generation. However, for general heat generation the domain must be divided into small areas in which distributions of the heat generation approximately satisfy the Laplace equation.