The Cosserat Spectrum theory is briefly summarized and applied to two-dimen
sional thermoelasticity. The discrete Cosserat eigenvalues and eigenvectors
of the first boundary value problem for a solid cylinder and a cylindrical
rigid inclusion in an infinite space are derived. The problem of uniform h
eat flow past a cylindrical cavity is reviewed within the frame of the Coss
erat Spectrum theory. The displacement fields caused by an arbitrary harmon
ic temperature field and a nonharmonic heat source around a cylindrical rig
id inclusion are solved by the Cosserat Spectrum theory.