The picosecond evolution of the plasma conditions in a laser-produced plasma was measured using a Thomson-scattering diagnostic. The picosecond resolved Thomson spectra was enabled by a pulse-front-tilt-compensated spectrometer. The Thomson spectra revealed a transition in the plasma conditions from an initially cold evolving plasma to a quasi-stationary equilibrium plasma. The equilibrium temperature was found to match the generalized heat equation's predicted scaling and . The plasma evolution was compared to Raman gain bandwidth calculations and showed a time-dependent resonance detuning that would limit the transfer efficiency of a Raman plasma amplifier in the linear regime.