Another issue is the energy of an atom doesn’t determine its temperature. Not exactly.

The high school definition of temperature as the average kinetic energy of the particles is merely an approximation appropriate only for gasses. Thusly the “ideal gas law”.

It’s better to think of temperature as a thermodynamic arrow. Heat flows from higher temperatures to lower ones. The rigorous definition of temperature is the inverse of the derivative of the entropy with respect to energy:

T = 1 / δS/δE

As you add more energy to a system, it gets more entropy, but because entropy is logarithmic it grows slower. So the derivative gets smaller. Thusly the temperature rises.

The flow of energy from high temperatures to low temperatures means that total entropy rises, because the system with lower temperature gains more entropy from the infinitesimal of energy. It’s how the universe obeys the second law of thermodynamics: Entropy always increases.