A fast approximation method to 3-dimensional equations in static and quasi-static uncoupled thermoelasticity is proposed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way, the action of the integral operators on such functions is presented in a simple analytical form. For densities with separated representation, we derive a tensor product representation of the integral operator which admits efficient cubature procedures. These results were obtained in collaboration with Vladimir Maz’ya and Gunther Schmidt.