The "Closed Cycle Nuclear Thermal Rocket Engine" is just a big nuclear steam engine that in this specific case, uses the (non radioactive) water steam to stay in air, at the height of the clouds, from which it captures the water to refuel its engines (assuming the clouds have enough water for that.
So, allowing for floating steam ships in a way.
A Thermal Nuclear Powered Rocket is basically a open nuclear reactor, where the coolant is heated by the enormous temperatures inside the reactor and expelled at absurd speeds (basically, a very dangerous steam engine).
Needless to say, this is a really dangerous way of propelling something on earth because of radioactive contamination, however, it is very safe to use once in space (because the atoms of the coolant are ejected so fast that they escape the solar system).
The solution would be to make a "closed cycle" system, where the coolant of the reactor would be used to heat a secondary coolant/propellant that would be expelled.
The only thing I could find relative to this was the "Nuclear Lightbulb", in which its nuclear core would heat up to 22.000 ºC and would heat the outer coolant/propellant with its hard ultraviolet emissions (thus, the nickname "lightbulb"). It is theorised to achieve a specific impulse (Isp) range from 1500 to 3000 seconds (15-20 kN·s/kg).
However, I would like to know about the possibility of using the closed cycle with something more akin to the ARE (Aircraft Reactor Experiment), which (I think) would be easier to to build calculate how much and for how long it would generate thrust with only the "steam" of the water of the clouds.
So, for how much and for how much and for how long this steam engine be able to lift a metal ship?
The first type of floating ship that I think of would be the "Sevastopol", from the game "Highfleet" since it has all the information necessary (in the link). But in that universe, they use pressurised methane. Of course, this is just an example, if you want to calculate something else of your choice, like a modern cruiser ship, I can't see a problem.