Thermodynamic currency?
The advantage of using a unit of heat is that it is a common standard anywhere in the universe, unchanging. Therefore, it's a good guide for physical process decisions anywhere. However, using it as a trading currency is subject to the same human valuation whimsy as any other currency.
We have a great need to be consistent evaluating the effectiveness of physical processes anywhere on earth. That comparison needs to be free of the relativistic shifts that accompany human valuation and trading.
Physical process measurements need to be weighted heavily in any human valuation system. But for trading purposes, an energy based currency would probably be pegged to something tradable, like a barrel of petroleum. However, the daily spot price of petroleum is apt to skyrocket should a sudden catastrophe greatly curtail the global supply, and the prices of other energy sources are now "sort of" tied to that price.
Giving priority to physical measurements runs deeper than simply changing the basis of a currency. For example, one local currency is pegged to a Kilowatt-hour from a wind farm, which encourages people to use that farm. Such ploys may help, but none are magic.