I'll venture the guess, that the explanation you read was wrong. What I'd find plausible is:
liquid mixed with gas has a higher effective thermal capacity - you don't need conductivity since the stuff is pumped through the cooling cycle, right?
What I mean by this: the liquid can receive a lot of heat by boiling. It carries the heat away not only in the form of higher temperature, but in the form of beeing a gas. In the other part of the cycle it can give away a lot of heat by condensing.
At least this is how heating works in dairy factories where I have been: when pasteurizing the big steel tanks, you pump vapour (with pressure greater than atmospheric, of course) in them, which condenses (therefore pressure drops, and more vapour is sucked in), which heats them very effectively.
The engineering problem in the cooling system is probably, that it's more difficult to pump such a mixture (like the blood in you veins, when delving upwards from a great depth too fast, might form bubbles and stop flowing, very dangerous). That's why it might be advanatageous, if all the liquid touching the engine gets evaporized, so you have no mixture, only arriving liquid and departing gas.
That are "educated guesses" which hopefully explain part of the surrounding physics. For a practical explanation of the occuring issues probably engineers are the better audience.