The recombination dynamics of zinc-blende-type, deep-red emitting CdTe/CdS core-shell nanocrystals is studied over a wide temperature range. Two characteristic decay regimes are found: a temperature-dependent decay component of a few nanoseconds and a long-living temperature-independent component of similar to 315 ns. The average decay time of the exciton states changes from 20 to 5ns when the temperature is increased from 15 to 295 K. At low temperatures, the observed decay behavior is assigned to thermally induced population and decay of the allowed exchange-split exciton states. At temperatures above T > 100 K, nonradiative decay channels involving phonons start to contribute to the exciton recombination. The observed broad distribution in decay times, monitored by stretched exponential fitting functions, we explain by variations in the electron-hole overlap caused by a partly incomplete CdTe/CdS core-shell structure and the nearly energy-degenerated bright and dark state superposition.