Sorry but there are plenty of systems in which a system's gravitational energy is related to its temperature. Example: ideal gases in a gravitational field whose pressures/densities at various altitudes are described by the barometric equation. Don't know where you're getting your info from, but it's no good.
From common sense: Temperature is a kinetic energy factor . . . gravity is a potential energy factor. Kinetic energy can counter potential energy . . . that's how we launch rockets.
From common sense: temperature has a more sophisticated meaning than what you're trying to attribute to it. How much do you know about statistical mechanics? Secondly, what the heck is an "energy factor"?
I agree . . . . Just trying to make the comparative concept simple . . . . . in a system involving temperature and gravity (among other things) temperature is 1 kinetic energy factor . . . . gravity is 1 potential energy factor. If you're more comfortable . . . just remove the "factor" references. It's not "rocket science"!