As far as I know (which isnt much) Global warming isn't really about heat released in systems. It's about its inability to leave the earth due to greenhouse effects.
While it is a concern if we produce a lot of extra heat, I think the main issue is being able to expect the heat to leave into space. Which is why most of climate change science focuses on greenhouse gases and not heat produced by machines.
No, not at all. The problem of AGW is not due to the calories we are releasing burning fossil fuels. It is because the waste byproduct of CO2 causing a slightly larger percentage of the sun's heat to be retained until the new, higher equilibrium temperature is reached where the trapped heat matches the heat the earth radiates.
Speaking of CO2. Capturing CO2 seems to be much less technically difficult than drilling 10 miles down. Various technologies already exist, and pilot plants are running. Perhaps focusing on the practical would be more productive than an illusory silver bullet.
It's not just CO2. It's CO2 and all the other greenhouse gasses.
And regardless, capturing them takes a lot of energy and unless we have a clean source (such as geothermal for example), that means that we will be releasing more greenhouse gasses than the produced amount of energy will capture.
It is far more efficient to not emit CO2 than to recapture it. It's worth doing the napkin math on how much air needs to be processed to undo one American's yearly CO2 footprint... It's a hell of a lot.
The thermal forcing from emissions are on the order of 20x the direct thermal forcing.
Any energy releasing process (nuclear, fossil fuel with ccs, geothermal) is bounded somewhere around 10-20x current energy use by running into direct thermal forcing.
PV produces less waste heat depending on where it is installed so has a slightly higher limit, but both solar and wind have pretty severe land use limits you run into at 20-100x current global energy.
Basically, everyone can have enough energy to flourish, but it's time to reign in growth and maybe dial it back a bit from US levels of consumption.