Thinking more on this, as I will want to resurrect the old system regardless of whether I replace it, so I need a plan of attack that doesn't involve fire extinguishers. There does seem to be a large body of evidence, from Internet posts, that the problem is specific to Molex/Sata splitters. The more I think about it, that is simply nonsensical, if the Molex was overloaded the fire would occur at the Molex, not at the Sata end.
But I have a theory... The Molex/Sata splitters generally seem to have quite short, stubby, leads. I have found in the past that when plumbing in Sata disks, the stiffness and weight of cable attached has pulled out a Sata cable or two, and the short stubby splitters may well make that problem much worse. I reckon a connector that was just and no more making contact, but not quite fully home, could easily find enough resistance to get hot?
What chance then, that this is behind the problem... that the fires are simply caused simply by foolish folks (self included) failing to make a proper final check on all connectors before putting the lid back on the PC?