Actually in thermodynamic terms temperature is a measure of how entropy (disorder) increases when you increase internal energy. Not the most intuitive definitio

Actually in thermodynamic terms temperature is a measure of how entropy (disorder) increases when you increase internal energy. Not the most intuitive definition (you can't just go and buy entropyometer for example ;)) but it works even when quantum effects kick in. And for ideal gas this measure happens to be proportional to the kinetic energy of the particles.