There is really no reason to think there is, or could be any problem in summer in the foreseeable future, since we are already in a worst case situation (highest temperatures ever recorded, basically no renewables used, nuclear as almost the only source of electricity at the moment) that is not problematic.
How about "most people aren't using electricity for heating"? People rarely heat their houses with electricity in Europe, that would be very expensive. It's usually gas or oil boiler, sometimes a coal one.
Edit: And coal heating is probably close to zero to be honest, that sounds old, even for the countryside. The rest of those 50% would be gas, petrol and wood.
https://b.radikal.ru/b12/1902/bd/a6d615dba25b.jpg
https://d.radikal.ru/d15/1901/1b/ea0e8c26f8d2.jpg
It gets much worse in the evening.
These photos were taken in Almaty, but the situation is the same everywhere (if not worse).
Most importantly it's a warning to other countries considering nuclear, especially equatorial ones where nuclear power is almost non-existent.
[1]not all of them though, in some cases the Rhône's flow wasn't enough for direct cooling and they went with cooling towers: The Cruas-Meysse plant has cooling towers and it's not affected by the current heatwave. Also, the Bugey and Tricastin plants have a mix of both (2 reactors with direct cooling and two with cooling towers) and only the reactors with direct cooling are affected.
Edit: having looked a bit more in details, it looks like even though the rivers can't be frozen to a point it stops the plant from functioning, the water admission systems can (partially) freeze in extreme weather and it happened a few time in France already.
Finnish plants have to reduce capacity during hot summers too, but it's because of their environmental requirements: the exhaust water back to the sea must not exceed a given threshold to protect marine life.
Nuclear plants could use warmer water, but regulation forbids them from releasing water at a higher temperature than 30°C.