  Anti-Stokes photoluminescence of metal nanoparticles, in which emitted
photons have a higher energy than the incident photons, is an indicator of the
temperature prevalent within a nanoparticle. Previous work has shown how to
extract the temperature from a gold nanoparticle under continuous-wave
monochromatic illumination. We extend the technique to pulsed illumination and
introduce pump-probe anti-Stokes spectroscopy. This new technique enables us
not only to measure an effective electron temperature in a gold nanoparticle
($\sim 10^3$ K under our conditions), but also to measure ultrafast dynamics of
a pulse-excited electron population, through its effect on the
photoluminescence, with sub-picosecond time resolution. We measure the heating
and cooling, all within picoseconds, of the electrons and find that, with our
sub-picosecond pulses, the highest apparent temperature is reached $0.6$ ps
before the maximum change in magnitude of the extinction signal
