I'm familiar with some civil nuclear power plants, my father worked for decades in the industry, and I did some internships too. (No contact with nuclear power on submarines / carriers)

All the designs I know of have a pumped (active) cooling loop for the reactor, then a secondary loop where the coolant (typically water) evaporates and drives a turbine, and that secondary loop is then coupled to either river water cooling or evaporation towers. (There might even be another intermediary cooling loop, not entirely sure).

(You don't want potentially radioactive water to interact with your turbine directly, makes it a nightmare to maintain).

> Also, I guess you could have the hot end very hot too..?

There are some limiting factors:

* melting point of your fuel (you really want that to remain solid, so you can control where it is)

* The reactor core is usually contained in a pressure vessel, which is made out of steel. Steel becomes weaker with higher temperatures. Switching to other materials is super expensive (harder to machine, fewer people are good at machining it etc.)

* You really want to be able to reliably move fuel rods and control rods in and out of the reactor; thermal expansion must be taken into account. At the same time, you want as little leakage as possible out of the reactor core.