Defect properties of Ce-doped and undoped ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ (YAG) crystals were studied by Doppler broadening of positron annihilation $\ensuremath{\gamma}$ rays and thermoluminescence (TL) as a function of temperature $(25--300\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})$. The positron diffusion length ${L}_{+}$ was evaluated mainly from the $S$ parameter versus positron energy. Compared with undoped YAG, Ce-doped YAG has a smaller positron diffusion length, due to its higher density of defects. ${L}_{+}$ in Ce-doped YAG decreases with increasing temperature up to $100\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, and then increases with temperature. The TL intensity in Ce-doped YAG shows the opposite behavior to ${L}_{+}$. The results indicate that point defects probed by positrons may be responsible for the energy transfer to Ce ions and TL intensity. Possible defects detected by positrons are negatively charged or neutral defects related to impurity antisites, cation vacancies, and vacancy complexes.