HELP! Electrical issues.
 

I have a 2004 s40 T5, i recently replaced crankshaft sensor, camshaft senso and a bad ignition coil ( replaced all coils less than a year ago). The single coil that was just replaced messed up and needed to be replaced (cylinder 3). I replaced it, and drove it 1 mile and it started missing bad. Got home, popped the hood and I see smoke and a sizzling sound coming for cylinder 3 coil, also noticed the negative battery cable had gotten hot and melted some of the Sheath on the wire. I looked it over and found the cable had corrosion inside. My question is could the battery cable issue be causing my coil to be getting hot?

did you measure your system voltage (ie too much voltage) ie if your voltage regulator allowing more than say 14.5V, then it seems plausible that could be a cause of too much power going to the coils and through the battery cable.? Note, usually when a battery cable gets hot and melts the insulation its because of internal corrosion in the cable itself (creating resistance and heat) so check the connectors and the positive cable feeling for any bumpiness... both may need to be replaced now.

What brand coils did you replace the (extremely reliable) Volvo coils with?