Fortunately that is not possible by any normal failure
method.
1) P3 had thermal shutdown, maybe it was an Athlon prior to
the motherboards having thermal shutdown.
2) Vinyl tubing doesn't melt at a very low temp, something
else was going on that was already a severe system failure
independent of the tubing. Might have been PSU, or
motherboard shorting out, CPU alone cannot create enough
heat to melt the solder on the heatsink, it would have far
sooner ruptured and PSU shut off.
3) PSU being crude /defective is the likely problem, any
normal PSU would shut down from overcurrent condition long
before delivering enough heat to melt solder on a heatsink
or melt vinyl tubing. It just isn't a realistic failure
scenario with any properly built PC, water-cooled or not.
4) As I've mentioned previously, the electrical wiring
insulation itself has no higher temp rating than the melting
point of vinyl tubing. If excessive temps are the problem
then we start drifting into the topic of lowest melting
point materials and rewiring everything with teflon wiring
but does anyone do that for a PC?
Regardless of the above I'd love to see those pics.