The photoluminescence (PL) properties of the Cu:Zn-In-S core quantum dots (QDs) and core-shell QDs were systematically investigated by using steady-state and time-resolved PL spectra at temperatures ranging from 80 to 400 K. The effects of the shell structure and the host bandgap on the thermal stability of Cu dopant emissions were studied by measuring the change in the PL intensity and the lifetime. It was found that the PL intensities and lifetimes of the core and core/shell QDs with green, yellow, and red emissions almost decrease with increasing temperatures while their PL was quenched at 300 K and 400 K, respectively, indicating the shell-enhanced thermal stability of the PL. The emission wavelength of the QDs as a function of temperature was also provided. The mechanisms of Cu dopant emission and thermal quenching were discussed. Finally, the green, yellow, red, and white light emitting light emitting diodes (LEDs) were fabricated based on Cu:Zn-In-S QDs.