So, we conclude that equating temperature and heat energy is like dropping the hammer over your toe and arguing in a movie that it will go up. Things that hit you are driven by energy. You can ignore physics by designing huge escalators in Vancouver, or the mass production of Tesla cars, but it always hits you in the end. All our major disasters come from ignoring basic physics, and it's an epidemic.
So although discussing physics makes you a "Poodle of the Oil Companies", let's plunge into it. Do not discuss this at elegant Trudeau cocktail parties. Do not discuss with trumpy bible thumpers on Facebook. It will get you thrown out.
There's lots of neat things to steal on the internet. This is classic heat conduction. The molecules start jiggling and then get their neighbours excited. This is a 'circular definition' diagram since it doesn't explain what the big Heat Arrow is. But it is just more vibrating molecules in the form of a hot gas (fire). Again the first molecule may have a high temperature, but almost no heat energy. When everything starts vibrating, then you have heat energy. The amount of that energy is the 'specific heat' times temperature. Very dense and loose molecules, like water, can hold an enormous amount of heat energy. Solid, dry rock holds very little. That is why deserts can be very hot in the day, and freezing at night. Lots of temperature, but no heat energy.
--to be continued