Multiply excited states in semiconductor quantum dots feature intriguing physics and play a crucial role in nanocrystal-based technologies. While photoluminescence provides a natural probe to investigate these states, room-temperature single-particle spectroscopy of their emission has proved elusive due to the temporal and spectral overlap with emission from the singly excited and charged states. Here, we introduce biexciton heralded spectroscopy enabled by a single-photon avalanche diode array based spectrometer. This allows us to directly observe biexciton-exciton emission cascades and measure the biexciton binding energy of single quantum dots at room temperature, even though it is well below the scale of thermal broadening and spectral diffusion. Furthermore, we uncover correlations hitherto masked in ensembles of the biexciton binding energy with both charge-carrier confinement and fluctuations of the local electrostatic potential. Heralded spectroscopy has the potential of greatly extending our understanding of charge-carrier dynamics in multielectron systems and of parallelization of quantum optics protocols.