Fitting a molten salt reactor to a ship is quite unlikely. The problem here is NOT the heat transport ability of the molten salt, which is indeed very high, but the very high amounts of moderator required tor this reactor to operate.
The limitations lie in the volume of the moderator i.e. the graphite (C) to fuel ratio. This is typically 10-12 times the volume of the fuel. In light water (H2O) moderated and cooled reactors, the fuel elements are typically tenth's of an inch apart. but in graphite moderated reactors, they are in the order of several inches apart, resulting in an enormous reactor core.
This is a characteristic also shared by heavy water (D2O) moderated reactors. Another is the ability to achieve criticality using natural uranium fuels without requiring enrichment (resulting in substantially cheaper fuel). Indeed the large volume and relatively low power density of these reactors allows refueling during full-power operation. This is not possible in light-water moderated reactors which must be dismantled for refueling.
It was for these reasons, 1) operation on natural uranium-based fuels and 2) the ability to add, remove, replace fuel at power that these reactors (graphite and heavy water) became the basis of designs of the poorer nuclear powers - Britain, France and India allowing them to make power and plutonium at the same time. Subsequent advances in centrifuge enrichment technology reduced this economic advantage.
Seen from the perspective of pure moderation (reduction of neutron energy by collision) graphite (C) is a relatively poor moderator vs light water (H2O). It requires many more collisions to reduce the neutron's energy to thermal levels. Fortunately, it also has much lower tendency to absorb neutrons, (typically capture via the (n, y) reaction). So it has a superior moderating ratio (number of neutrons moderated over number captured).
But it is a bulky moderator. No graphite moderated reactor has ever been used on a ship to my knowledge.
Soviet reactors designs using a molten metal lead-bismuth coolant are an entirely different type of reactor, which has NO moderator and are in fact FAST reactors.
