If a river is smaller then it thermally approaches the surface soil temperature and is more subject to small changes in topology.

If it is larger more of it has more thermal isolation from not only the sun but also the ground. Since most water comes from elevation or “cool mountain streams” or melt, this is a factor, along with the time to get to the sea, because a larger river can carve and maintain a more direct route. It can also be deeper, so more of it is shaded from the sun by the materials it carries.

Deliberately shading it might be an option but a living river is also dependent on photosynthesis so…