This should also be affecting coal plants, since they also need to exhaust heat via an identical mechanism. Yet the article only mentions nuclear.
But do you have numbers on how it's affecting coal plants? Maybe coal plants don't need so much cooling?
You don't shut down your nuclear plants, you moderate them up and down.
Unlike e.g. Germany, France's nukes were designed (and are used) for very aggressive load following, reactors can output 30~100% of their rated power and can rate up and down at up to 5%/minute.
Here's a twitter thread on the subject (in french) from early march: https://twitter.com/TristanKamin/status/1102620969808658432
This is a bloke who apparently likes following france's electrical and nuclear networks, roughly speaking on March 4 checking the previous week's data they saw that only 40 out of 50 reactors had been running (= more than 50% of rated power) on sunday, looking at electical demand it had fallen 15GW from early feb to early march (march was quite warm), nukes had dropped 10GW between saturday and sunday: not only was demand low (usually the case on french sundays) wind power had gone crazy. Gas plants were completely shut down (except those used for both electricity and heating), hydro was at the lowest possible level, pumped hydro had pumped all it could.
Checking neighbours, Germany and Austria had spent part of the weekend with sub-zero electricity prices (they were paying surrounding countries to take electricity off of their hands).
From sunday to monday, demand picks up like mad, and the nuke network handled overall increases of 50~100MW/mn over the morning (it still had to be supplemented by hydro and gas as consumption rate of changes exceeded 150MW/mn).
This is the graph of nuclear production changes over the week-end: https://twitter.com/TristanKamin/status/1102625880520699911/... the sunday lows went down below 38GW, the highs on either side are above 50.
Coal plants are air cooled, not water cooled (i.e. they have exhaust), and are not affected.
https://en.wikipedia.org/wiki/Fossil_fuel_power_station#/med...
Exact same evaporative cooling towers as used in nuclear power plants, which is what you'd expect seeing as they use the same steam turbines to drive their generators.
And a diagram of a generic coal power plant:
https://en.wikipedia.org/wiki/File:Coal_fired_power_plant_di...
Again, water cooled.
https://allthingsnuclear.org/dlochbaum/shh-secrets-of-the-co...
They cool the water, not the plant.
Cooling towers cool water because it was heated up in some way, possibly by cooling the power plant.
Coal plants typically only have the tower, and don't use river water.
Coal plants can certainly use ponds to cool, but air cooling works just fine for them. Unlike Nuclear Coal can eject most of its heat, as exhaust from burning the coal, into the air.
I have to add, it was a little dishonest of you to link to the one photo with cooling towers, and not to all the other ones that don't have them.
It's the first picture on the page "Fossil fuel power station", which is the redirect for "coal power plant".
The second photograph is Currant Creek Power Plant, which is a relatively modern (2005) gas-fired plant, which does indeed use air cooling.
The third photograph is the decommissioned coal-fired Carbon Power Plant. Although not clear from the photo, this uses water cooling. The cooling towers are visible here:
https://www.deseretnews.com/article/705396191/New-mercury-st...
The fourth photograph is the decommissioned coal-fired Mohave Power Station. This also uses water cooling, although its cooling towers are shorter and wider than the classic hyperboloid design.
Fifth is the active Taichung Power Plant, coal-fired, also water cooled according to its Wikipedia page.
100% of the photographs of coal power plants on the page reached by searching Wikipedia for "coal power plant" show water-cooled plants. How is my example dishonest?
Cooling towers are specifically when you don't use river water for cooling.
Your first photo has a large lake in front of it, so clearly they will use that, but the rest don't, they only have the towers.
Nuclear plants almost always use once-through cooling or cooling ponds, but coal plants typically don't, and are unaffected by the heat limits (which are environmental for fish, not technical for power generation).
Edit: Notice how in the diagram you linked there is a river for cooling, but there is no tower? Coal plants will have one or the other, but nuclear uses both, and that's because most of the waste heat from coal goes up the chimney.
>but nuclear uses both
People have already posted multiple examples of nuclear plants that use only one, e.g. https://news.ycombinator.com/item?id=20532670