Time dilation also applies to a slightly different time than Newton's time. It turns out this is the more foundational definition of temperature, and the other

Time dilation also applies to a slightly different time than Newton's time. It turns out this is the more foundational definition of temperature, and the other one (average kinetic energy) is mostly a useful heuristic that matches well under certain conditions (like when the distribution of energy is close to the Boltzmann distribution), but not others (a very fast-moving baseball).