This work uncovers the thermal properties of colloidal CdSe/CdS quantum dots (QDs) associated with additional epitaxial strain at the core/shell interface. We investigate the temperature-dependent behavior of the longitudinal optical (LO) phonon frequencies of these QDs by Raman spectroscopy over a temperature range of $7--300\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. For wurtzite and zinc-blende structured QDs, a characteristic redshift of the CdSe and CdS LO frequencies with increasing temperature is found. The extent of this redshift, however, depends on the interplay between the two materials in the heterostructure as well as on the temperature. We propose a simple method to separate the pure thermal properties of each material from characteristics determined by the interaction of core and shell. Thereby, it is possible to determine positive thermal expansion coefficients of CdSe and CdS in the temperature range of $7--300\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with high accuracy.