A thought exercise: If all of the world’s power plants were converted to nuclear, would the waste heat from the reactions heat up the planet in any significant manner, wreaking havoc on the environment?
I am thinking that since the energy is coming from the atom, rather than from the sun, we would be introducing unnatural net levels of heat on the planet’s surface. Or would the heat generated not be enough to create any harm?
At least in theory, you’d be reducing our current production of greenhouse gases. So you’d probably get a net reduction in global warming. The planet is reasonably good at radiating waste heat – look at how quickly even a warm day cools down at night.
No more so than coal or any other fuel-burning power plants, AFAIK. The only difference (well, the primary difference) between nuclear and other types is the source of heat, which is used to boil water, producing steam, which turns the turbines. As in other processes waste heat equates to loss of efficiency, so it’s in the best interest of the power company to capture as much of the reaction heat as possible, to convert into electricity.
It’s hard for me to picture the answer on such a grand scale, but I can say that power plants study (model, consult experts, etc.) heat rejection and the related environmental impact to neighboring, natural bodies of water, for one…including operations during drought conditions. (The grand scale answer just might be scary!)
In general, large bodies of water, cooling ponds, and/or the atmosphere are considered “heat sinks”, in the field. A “perfect” heat sink (the ideal) can take in an infinite amount of heat rejection without it, itself, experiencing any rise in temp. Of course, the ideal heat sink does not exist in reality.
To start to answer this, I guess if we took the average heat rejected (BTUs/hr)from the average nuclear plant and multiply it by the number of plants one foresees per the OP…we could find a total rate of heat rejection (BTUs/hr). We might even assume it is all lost eventually (directly or indirectly) to the atmosphere. Then, knowing the rate at which heat dissipates from the atmosphere on a (pre-defined) “average” day (BTUs/hr), we might start to answer this question. This is oversimplifying the problem, but a start for some food for thought.
FYI: Along these lines, it worth mentioning this: I believe it was “Nova” or the “Discover” channel did a reoprt about what is known about harnessing the energy from nuclear fission. The show confirmed my suspicion that people claim they would “run so clean” only because their waste products are not yet defined in the scope of everything written to define and legislate waste products! In other words, if such a plant could operate tomorrow, it would leaps and bounds ahead of the legislation needed to regulate its (new form of) waste!
Off the top of my head…or just going out of my head 
Did you mean to type “fusion”, there? Fission is what we already have.
And I’ve never heard tell of any “waste products” from fusion, other than helium. Is helium considered hazardous now?
Fossil fuels’ energy content was originally derived from the sun; but so many millions of years ago, and burned at so much faster a rate than it’s being formed, that for all practical purposes it’s simply added energy to the Earth’s current heat balance. No real difference whether it’s nuclear or fossil.