A high cadence shouldn’t make you any hotter than a low cadence with the same effort level. If you are getting hot with a high cadence then I’d suspect you are achieving the higher cadence partly by peddling harder rather than finding an appropriately easy gear.
Where did I say it had nothing to do with how far you can go? You choose your cadence by choosing the gear you us.
But mountain bikes are generally heavier than road bikes, and they do have significantly higher rolling resistance. Not to mention you are less aerodynamic on a mountain bike. Those are the reasons you get more tired on a mountain bike than on a road bike for a given distance.
I get hotter because I’m not in the wind. That requires lower power output: I set the gear and cadence not to maintain the same power output: I set the gear and cadence to maintain a lower power output.
Spinning at high cadence is not an effective strategy for me: I find I do better slightly lowering the cadence when I’m spinning.
This might be old-school – I am old.