If you give people a generator that produces "cheap and plentiful energy"? Absolutely. Total world power dissipation increases as fast as they can build the plants. If we never produce another molecule of CO2 again we might be okay in that situation, but things like that don't change overnight.
Rough order of magnitude calculation, the Earth receives about 1000W/m^2, that's 6370km^2 * pi * 1000W/M2 ~ 1e17W, and according to Wikipedia the global energy use of humanity is 7050 millions tons of oil equivalent per year so 7050 * 11.63TWh / 1year ~ 1e13W. So we have about 4 orders of magnitude of difference here. Does the human heat output make any difference? Probably not.
Hardly. The amount of energy trapped by the atmosphere is vastly greater than the heat capacity we would wish to be able to produce, and the corollary - the amount of energy irradiated by the earth into space is vastly greater than amount of heat we wish to produce.
And it was balanced, so it doesn’t matter if it’s fifty terrawatts or fifty million. What matters is:
> The growth in Earth's energy imbalance from satellite and in situ measurements (2005-2019). A rate of +1.0 W/m2 summed over the planet's surface equates to a continuous heat uptake of about 500 terawatts (~0.3% of the incident solar radiation).[2][35]
I found a chart that says we’re producing about 25,000 TWh per year of power now, or 2.9 TW continuous to put it in the same units. But what is the efficiency of those plants? 35%? That’s 8.3 TW of heat, which is already 1.6% of our budget surplus. If we dogleg our energy production while thinking it virtue signaling, that quickly becomes 5% of a number that is slowly cooking us. That brings doomsday in by years.
We can’t endlessly dump heat into the atmosphere any more than we can continuously dump mercury into the oceans.
In your equation above. The sun produces so much more ambient heat I imagine everything else is a rounding error. I highly doubt any number of fusion plants would affect global temperature.
I’m getting 1.6% of our heat surplus at present power production rates, and I’m saying what if we triple our power production because it’s cheap and clean now?
Wind doesn’t increase this number. Nor does hydro. Solar only does if the albedo is lower than ambient. Tidal… I wouldn’t even know where to start calculating that. Heat engines increase it by something like 300% of the power that gets to your light switch.
edit: conclusion
edit again: I'm extrapolating from https://en.wikipedia.org/wiki/Jevons_paradox but didn't remember what it was called