A thermoelastic model is proposed to determine elastic strain effects on electronic properties of spherical Type I and Type II heterostructure core/shell quantum dots (QDs) as a function of dimensions of constituent semiconductors at any temperature. Proposed model takes into account the difference between lattice constants, linear expansion coefficients and anisotropy of elastic moduli (Young's modulus and Poisson's ratio) of constituent semiconductors, respectively. In analogous to lattice mismatch, we introduce so called the elastic anisotropy mismatch in heterostructures. Compressive strain acting on core (shell) side of heterointerfaces in CdSe/CdS, CdSe/ZnS, and ZnSe/ZnS QDs increases (decreases) as shell diameter is increased, which causes increase (decrease) in core bandgap as sell (core) diameter is increased in these nanostructures. Furthermore, there is a parabolic increase in conduction band offsets and core bandgaps in CdSe/CdS, CdSe/ZnS, and ZnSe/ZnS QDs and decrease in conduction band offset and core bandgap of ZnSe/CdS QD as core (shell) diameter increases for fixed shell (core) diameter. Comparison shows that using isotropic elastic moduli in determining band offsets and core band gaps gives better agreement with experiment than anisotropic elastic moduli for core bandgaps of CdSe/CdS, CdSe/ZnS, ZnSe/ZnS, and ZnSe/CdS core/shell QDs. Furthermore, we also show that the strain-modified two band effective mass approximation can be used to determine band offsets by using measured core band gaps in core/shell heterostructure QDs with Type II interface band alignment. Excellent agreement between predicted and measured core bandgaps in CdSe and ZnSe based core/shell QDs suggests that proposed model can be a good design tool for process simulation of core/shell heterostructure QDs.