I have wondered about this scenario for a while, and would like to know what is your opinion about it. Its assumptions are quite specific and probably won't be true, but they do appear realistic enough for me.
(1): Assume that nuclear fusion becomes an available energy source within a couple centuries, it will provide a cheap, plentiful, emission-free, and long lasting source of energy for human activities.
(If this assumption is wrong, we are probably in trouble)
(2): Assume that continued economical/technological development requires increasing energy consumption indefinitely.
(This is probably wrong if we utilise completely new physics in the future, but I don't think this assumption is unlikely)
(3): Assume that the generation of waste heat during energy generation/consumption cannot be dramatically lowered in the short-term future.
(This is also probably wrong. But it will hold true if we still have to use machines/engines/generators based on the same design principles as we do today, and I don't see that happening too soon)
The logical conclusion from the above three assumption:
At some point after the implementation of nuclear fusion, humanity's energy consumption might reach a level so high that the waste heat we release into the atmosphere will be altering the Earth's climate system not unlike what our carbon emissions are doing today.
(Since the source of any future fusion plant is likely hydrogen in seawater, for Earth it probably acts as an extra heat source independent of the sun)
The Earth is functionally a giant spacecraft, and spacecrafts usually have very sophisticated heat management systems to prevent them from overheating, so perhaps we have to work with that as well.
I haven't done too much number crunching yet, I might have gotten the figures wildly wrong.
We know today the amount of solar energy the Earth receives per year is about ~5000 times the amount of energy humanity consumes.
If humanity's energy consumption increases 100 times, and 50% of the energy is released into the atmosphere as waste heat, then we are releasing ~1% of solar energy into the atmosphere as heat.
That might have some serious climate implications if lasting for a long time, but I'm not certain about that yet.
(1): Geoengineering, that seems to be obvious. We try to reduce the solar energy input on Earth when the heat we release is too much. But that probably will negatively impact the biosphere a lot due to photosynthesis issues.
(2): Set "energy consumption targets" for countries/firms/etc like current climate policy.
Problem: while countries can continue to develop their economy and technology without increasing carbon emission (by adopting clean energy, etc), a limit on energy consumption seems be a hard cap on a country's development that cannot be worked with. So, probably no one would be compliant with such an agreement...
(3): Colonising other planets/solar systems
Each colony would also have to face that problem.
The Earth (and any other planet/moon we colonise) seems to be functionally the same as a giant space station. And space stations need sophisticated maintenance systems, including management of waste heat.