Why did my PSU wire catch fire?

Just been building my PC up again after my old motherboard failed. I was tinkering around trying to stop it from blue-screening during Windows install when on the 6th restart or so, suddenly clouds of smoke start billowing out of the PC on my lap. At first I thought it was the CPU because I'd just add more thermal paste to it and couldn't get the fan back on tightly enough. When I looked closer, the whole length of one red wire from the PSU had completely charred and the plastic had melted. It was one of four or five wires connecting to a few molex plugs which weren't connected to anything at the time. My dad's opinion is that it somehow shorted against another wire or something. He suggests I cut off all the wires to them molex plugs and tape each end to prevent them shorting again. Will that be okay to do, if I don't want to replace my (expensive 1000W) PSU?