Multiple exciton generation (MEG) in semiconducting quantum dots is a process which produces multiple charge-carrier pairs from a single excitation. MEG is a possible route to bypass the Shockley-Queisser limit in single-junction solar cells, but it remains challenging to harvest charge-carrier pairs generated by MEG in working photovoltaic devices. Initial yields of additional carrier pairs may be reduced due to ultra-fast intraband relaxation processes which compete with MEG at early times. Quantum dots of materials which display reduced carrier cooling rates (e.g. PbTe) are therefore promising candidates to increase the impact of MEG in photovoltaic devices. Here we demonstrate PbTe quantum dot-based solar cells, which produce extractable charge carrier pairs with an external quantum efficiency above 120%, and we estimate an internal quantum efficiency exceeding 150%. Resolving the charge carrier kinetics on the ultra-fast timescale with pump-probe transient absorption and pump-push-photocurrent measurements, we identify a delayed cooling effect above the threshold energy for MEG.