We report on an experiment irradiating individual argon droplets of 20 μm diameter with laser pulses of several Joule energy at intensities of 1019 W/cm2. K-shell emission spectroscopy was employed to determine the hot electronenergy fraction and the time-integrated charge-state distribution. Spectral fitting indicates that bulk temperatures up to 160 eV are reached. Modelling of the hot-electron relaxation and generation of K-shell emission with collisional hot-electron stopping only is incompatible with the experimental results, and the data suggest an additional ultra-fast (sub-ps) heating contribution. For example, including resistive heating in the modelling yields a much better agreement with the observed final bulk temperature and qualitatively reproduces the observed charge state distribution.