One thing I'm curious about to see quantified (I'm sure this has been done, but don't know where to look): If you burn a gallon of gas, it immediately releases some quantity of heat into the environment, this becomes heat pollution regardless of how the energy is used. The CO2 then joins the atmosphere and contributes some marginal change in the balance of energy of the atmosphere by inhibiting radiation of energy into space, this can be expressed as an amount of power (greenhouse effect power). There is some amount of time (greenhouse breakeven time) where these effect balance each other out, and the amount of greenhouse effect power * time is equal to the initial energy released. After that point, the greenhouse impact becomes larger than the impact of initial energy released and the greenhouse term matters. I did some really rough calculation of this time period and got ~ 1 year.

If total CO2 in the atmosphere were at equilibrium (it is not currently), there would also be a mean amount of time for CO2 to be sequestered. The ratio of (mean CO2 time / greenhouse breakeven time) would exactly characterize how much worse for the climate energy sources with carbon emissions are relative to zero carbon sources in terms of the total contribution of heat into the environment. With CO2 not at equilibrium, there is probably some fancier model to get a similar characterization.

Finally, it would be interesting to see quantification of different sources of renewable power in terms of thermodynamic impacts. For example, I would expect that solar would lead to energy that would otherwise likely be reflected back to space instead be dissipated into heat. It would probably for example be worse to have a planet that is entirely covered with black solar panels from a radiation perspective. On the other hand, for something like hydroelectric or geothermal, it would seem like we are simply channeling a energy source that is already just about to be dissipated into heat on its own.