Could waste heat become an environment problem in the future (centuries)?

Back-of-the-envelope equilibrium estimate: if we increase the energy added to the atmosphere by 1%, then the Stefan-Boltzmann law says that a blackbody would need to be ${0.01}^{0.25}$ warmer, or 0.4%, to radiate that much more. At the Earth's temperature of ~288 K, this would be ~0.7 K warmer.

This suggests to me that it will have a smaller impact than global warming. Whatever we use to solve global warming will probably work on this problem as well. It's still something to keep in mind, though.

See this more rigorous analysis by Robert A. Freitas. Yes, it will cause some problems.

There's a post about this at the blog DoTheMath, which calculates we boil ourselves with waste heat in ~400 years, assuming GDP doubles every 100 years and per capita energy consumption increases at the same rate it has been for the previous ~400 years.

The usual economic retort is that the economy could look very different from the one we are used to, and decouple from energy consumption. But the assumption about waste heat is what is doing the work here, and we have recently developed thermal transistors. These transistors have been designed out of quantum objects. And it turns out we might be able to beat the Planck limit in the far field. Which is to say, we can build heat computers, and then waste heat could be converted into computation.

That doesn't solve the problem of too much energy use being bad, but if waste heat is computation then we can hit peak (safe) output, stay there, and still add value.

It possible to create a sphere out of mirrors around our earth that can be turned to reduce the amount of energy earth receives from the sun. It's very expensive to build such a system but I would expect it to be build if we get heat problems a few centuries down the line.

Geoengineering includes getting better at radiating heat as well as reducing heat received. Superconductor to dark-side cold farms might do the trick. Also, include bioengineering in your list of possible mitigations: if we can live in a very hot environment (or upload/emulate on a more durable substrate), it's less of a problem.

Longer-term, #3 is the only way. Intelligent life needs to elsewhere when this planet's used up.

I don't expect this to be a problem because by the time humans would be using this much energy we should be easily capable of constructing simple megastructures. One would only need to decrease the amount of IR light that hits the earth with massive but relatively cheap (at least once you have serious space industry) IR filters in order to decrease the earth's temperature without impacting anything dependant on the sun's light.

reversible computer gates exist and are Turing complete, which in human words means it's possible to do computers where the elections are not sent to ground willynilly. When you "not" a live wire, that in a very real sense is sending elections to ground.

Now I think Turing completeness is a terrible standard, we really need a more complex hierarchy like complexity thoery has, as my understanding of the proof these things are Turing complete is that they are generating waste outputs, so if you are stopping using not gate to prevent sending elections to ground and you generate waste outputs that in thoery your sending to ground there is not nesserily an improvement here, but maybe something comes out of it anyway.

Futher more if we have fusion don't we have economical carbon sinks? And space sillyness?

I'd like to question both assumptions (2) and (3).

For (2), it's not clear to me that "more energy" is the thing people want. Some things we do require a lot of energy (transportation, manufacturing) but some things that are really important use surprisingly little power (the internet).

For (3), it seems like we've been moving in the direction of more-efficiency for a long time (better engines and turbines to convert more of the fuel into useful energy, fewer losses to friction and transmission, etc.).

Overall, I think we're seeing an upward trend in power usage because more people are getting the full benefit of modern technology, not because modern technology is using more power per person. I wish I could find a long-term graph, but per-capital power consumption in the United States has been going down for a few years, and total power consumption in the United States has been flat since around 1995: https://en.wikipedia.org/wiki/Energy_in_the_United_States#Consumption Another way of putting this is that it's not that cars are using more gas, it's that a lot more people have cars. This means that in the short-term we can expect energy usage to continue going up for a while, but it could plausibly peak if/when the global population peaks and we finish the project of ending worldwide poverty.

For (1) I could nitpick since fission could also power our civilization for a long time, although I don't think it really effects the question you're asking.