While the Motie superconductors are referenced several times in The Mote in God's Eye, their use to distribute heat around a spaceship hull (and therefore avoid burn-through) is not referenced until The Gripping Hand. The trick with the superconductor running through a water tank to cool a ships superconductor coated hull is first mentioned by Freddie Townsend in chapter 7 of The Gripping Hand:
"Anyway, when we dive near a sun to get a gravity assist, I don't want solar radiation sleeting through Hecate, so I mounted this mucking great water tank alongside the cabin for a shield. And I freeze it. Then the hull's superconducting, of course, so I can cool the hull by running a wire into the water tank. I can do serious aerobraking or get awfully close to a sun because it can't fry us without first boiling all that thermal mass of water, and even then I can vent the steam."
That book came out in 1993, so it's entirely possible that you've read this when you were younger. It wouldn't make sense for this to be in The Mote, since humans just discovered the heat superconducting material and at no point in the story did humans fire upon a Motie ship, only on the Watchmaker improved MacArthur and her expanding Langston Field (which was a different trick from the superconducting hull).