We measure intensity-dependent changes in the nonlinear optical scattering from individual Au nanorods excited with ultrafast laser pulses at their plasmon resonance frequency. Isolating single rods allows the measurement of a greatly enhanced nonlinearity compared to nanorod ensembles or bulk Au. Surprisingly, the ultrafast nonlinearity can be attributed entirely to heating of conduction electrons and does not exhibit any coherent effect associated with plasmon oscillation. This suggests a previously unobserved damping of strongly driven plasmons.