We report an experimental study of the emission statistics of excitonic complexes from a single quantum dot and their temperature dependence. The single photon emission from the exciton ground state is shown to persist up to 80  K. The deterioration of single photon statistics is attributed to new biexciton emissions, which emerge in the vicinity of the main single-exciton peak at rising temperatures. We identify these biexcitonic states as being formed by either one hole or two holes occupying excited states and analyze their specific polarization and power-dependent signature.