The Cosserat Spectrum theory is briefly summarized and applied to two-dimensional thermoelasticity. The discrete Cosserat eigenvalues and eigenvectors of the first bound ary value problem for a solid cylinder and a cylindrical rigid inclusion in an infinite space are derived. The problem of uniform heat flow past a cylindrical cavity is reviewed within the frame of the Cosserat Spectrum theory. The displacement fields caused by an arbitrary harmonic temperature field and a nonharmonic heat source around a cylindrical rigid inclusion are solved by the Cosserat Spectrum theory.