Time-resolved K(α) spectroscopy has been used to infer the hot-electron equilibration dynamics in high-intensity laser interactions with picosecond pulses and thin-foil solid targets. The measured K(α)-emission pulse width increases from ~3 to 6 ps for laser intensities from ~10(18) to 10(19) W/cm(2). Collisional energy-transfer model calculations suggest that hot electrons with mean energies from ~0.8 to 2 MeV are contained inside the target. The inferred mean hot-electron energies are broadly consistent with ponderomotive scaling over the relevant intensity range.