What a brilliant display of capitalism making the heating problem ever worse while thinking it's fixing it, Will.
Emissioms are not the issue, they are a symptom, a multiplier, and a distraction from the main issue, which is that we are taking things from the Earth and converting them to heat where there was no heat, and this is adding to the heat from the energy of the sun, which we are not using to create anything other than heat.
And what is it for - to make profit for some frenzied investors panicking because they are running out of "safe" things to invest in.
Whilst this thing called profit is an energy lie, a trick that returns more energy back than was put out, in the form of money.
The energy in profit has to come extracted from the planet, because the planet is the only thing that responds to a little energy put in, with more out.
This is energy extraction, from the planet, with the same by product as always - heat, much more energy is lost to heat than is yielded to profit.
So as long as we need and seek profit, there will be heating, and this is a direct relationship, not time related, it's profit related.
Sorry to put the dampers on any investor hype, but this the reality, the business of capitalism based on the energy lie of profit is what needs to stop, to stop the destruction, stop the heating, stop rewarding for destroying and heating.
Invest in powering up your own communities, governments businesses, by solar, do enough to disconnect from the grid, stop rewarding it for extracting all it's energy from the planet, the energy it needs to make its profit. Issue solar indexed stimulus to empower it all whilst putting solid energy value into money. Dump all excess peak energy into hydrogen. All of this cools it's all creation, converting the energy of the sun to things other than heat.
The "energy density" function you mention is only relevant to the for-profit scenario, it's only needed to satisfy bunches of investors seeking profit, it isnt needed for all businesses and communities solar powered, and can't be had, because the energy of the sun is distributed by nature, but it's huge if, and when we all collect it, and put it to use as things other than heat, like hydrogen which actually does have 3x enetgy density of fossil fuels in the same state, we could easily create enough of that between us to keep all aerospace airborne, even bringing back things lost, like reusable space shuttles, supersonic commercial flight, and it would by flying 3x further than was done by fossil fuels, given we will quickly learn how to liquefy it at room temoerature - reaearch obvious by omission which appears to have been cancelled by fossil fueled interests, we will have all of this by community based solar hydrogen as soon as investors and money issuers might agree this would be the best investment we could ever make, and we empower it, with the required funds to do it - solar indexed stimulus for all people.