In this chapter, we consider three thermoelastic optimization problems. We look at the optimal thickness distribution for a beam of variable thickness, when the goal is to maximize its resistance to thermoelastic buckling, or in other words, to maximize the critical temperature at which buckling occurs. In the second problem, we allow the beam to be constructed inhomogeneously, looking for an optimal distribution of materials that maximizes the critical temperature. The third and final problem concerns heat conduction in locally orthotropic solid bodies. By locally orthotropic, we mean a particular type of inhomogeneity, where the principal directions (axes of orthotropy) may vary as a function of the space coordinates. We derive a guaranteed double-sided estimate for energy dissipation that occurs in heat conduction in a locally orthotropic body, without assuming anything about the material orientation field. This yields guaranteed lower and upper bounds for energy dissipation that always hold regardless of how the local material orientation is distributed in the solid body.