This study presents new structural formulas for steady-state thermoelastic Green's functions (TGFs) to a plane-generalized boundary value problem (BVP) of thermoelasticity for a generalized half-strip. The structural formulas for TGFs are expressed in terms of Green's functions for Poisson's equation (GFPE). These results are formulated in a special theorem, which is proved using a developed harmonic integral representations method. The development of this method consists in calculating a boundary integral of the product between two GFPEs. This integral was calculated due the proved before statement that the TGFs have to satisfy must have the following two conditions: (1) thermal boundary conditions with respect to points of application of the heat source, and (2) mechanical boundary conditions with respect to the points of finding the displacements. On the basis of derived structural formulas, it is possible to obtain many explicit Green's functions for termoelastic displacements, deformations, and stresses. An example is presented for a concrete-plane BVP for a half-strip; TGFs are obtained in terms of elementary functions. New analytical expressions for thermal deformations and thermal stresses to a particular plane problem for a thermoelastic half-strip under a boundary constant temperature gradient were obtained. The graphical computer evaluation of thermal deformations and thermal stresses, created by a unit point heat source and by a temperature gradient, also is included.