Hmm, if your connectors were crap then you'd get less current and so less heat. Something in your system is drawing too much power. They tend to do that when they get too old.
I suppose you could always polish the connector pins a bit (carefully!) and get new power feed cables. If you cpu card has a fan you might be able to take some of the load off the motherboard by powering the fan straight from the PSU (if it's not already).
I have this problem with my Amiga too, and I never really managed to fix it. Without the two extra powerfeeds (one in the fan, one in the floppy power feed), my Amiga probably wouldn't work at all. :-(