A precise knowledge of the temperature and number of hot electrons generated in the interaction of short-pulse high-intensity lasers with solids is crucial for harnessing the energy of a laser pulse in applications such as laser-driven ion acceleration or fast ignition. Nevertheless, present scaling laws tend to overestimate the hot electron temperature when compared to experiment and simulations. We present a novel approach that is based on a weighted average of the kinetic energy of an ensemble of electrons. We find that the scaling of electron energy with laser intensity can be derived from a general Lorentz invariant electron distribution ansatz that does not rely on a specific model of energy absorption. The scaling derived is in perfect agreement with simulation results and clearly follows the trend seen in recent experiments, especially at high laser intensities where other scalings fail to describe the simulations accurately.