That is untrue. They have the same cooling requirements as all thermoelectric power plants do, and some like eg. Diablo Canyon do straight up boil water away. Others heat up lakes or coastlines - which costs (more plant, land and maintenance) and can only be done in some places [1]. Plants cooling requirements are a big part of their overall cost, even with the legacy environmental protection which has led to our current crises.
[1] - https://www.ucsusa.org/clean-energy/energy-and-water-use/wat... Types of cooling
( https://iopscience.iop.org/article/10.1088/1748-9326/7/4/045... )