The fluorescence of single colloidal thick-shell CdSe/CdS nanocrystals (NCs), at cryogenic temperature (4 K) and room temperature (RT), is studied using the intensity autocorrelation function (ACF) and lifetime measurements. The radiative and Auger decay rates corresponding to the desexcitation of the charged biexcitonic state are determined through an original method of photon postselection. Especially, the charged biexciton quantum yield increases from about 15% at RT to 60% at 4 K. The high inhibition of Auger recombination already observed for the trion state of CdSe/CdS NCs at low temperature is also demonstrated for the charged biexcitonic state. At 4 K, the ACF is equal to 1 for time scales ranging from 50 ns to 200 ms. In contrast with RT operation, the intensity of the trion emission is then perfectly stable and no blinking is observed. All the results highlight the strong confinement of the charge carriers in the CdSe core.