We report femtosecond stimulated Raman spectroscopy (FSRS) measurements on dispersions of CdSe semiconductor nanocrystals (NCs) as a function of particle size and pump fluence. Upon photoexcitation, we observe depletion of stimulated Raman gain corresponding to generation of longitudinal optical (LO) phonons followed by recovery on picosecond timescales. At higher fluences, production of multiple excitons slows recovery of FSRS signals, which we attribute to sustained increases of LO phonon populations due to multiexcitonic Auger heating. Owing to the discretized electronic structure of these NCs, such heating cannot be readily monitored via electronic spectroscopic analysis of high-energy band tails as has been performed for higher-dimensional materials. Notably, recovery timescales exceed those of the biexcitonic Auger recombination process and as such reveal overall thermalization timescales likely owing to an acoustic phonon thermalization bottleneck that dictates the cooling timescale.