The theory of thermoelasticity takes into account the coupling between elastic stresses and temperature, cf. [BSS89, Now75, Kög00]1. We present first the fully coupled theory where the interaction between temperature and mechanical forces is taken into account. The equations are linearized and the heat conduction is modelled by Fourier's law. Then, several simplified models under additional assumptions are investigated. For all these problems, the Fourier fundamental solution and the BIE are derived. Fundamental solutions in the original space are only available for very special cases.