I've been through this with my 2000 V70-- the positive battery cable was getting hot to the touch and I measured a significant voltage drop between the alternator output and the voltage across the terminals, indicating that that cable needed to be replaced.

I read elsewhere that the aftermarket OEM replacement cables weren't very good quality, and the pricing on the genuine Volvo ones was outrageous: about 3x the aftermarket cost. I was planning on fabricating one (the only thing that is special about it is the post with the 10mm nut to attach the B+ cable), but I ended up spotting a new genuine Volvo one in a pick-and-pull and used that instead.

Others have suggested having a cable fabricated at a place that does marine electric work.

Good luck!

Can you tell if the copper portion of the cable is thinner? Or perhaps just the insulation is thinner?

Improvements in insulating materials has made some of them to be thinner. This has caused concerns when wires are pulled through conduit that the thinner insulation may not hold up to the abuse of pulling the wires.

Can you see if the strands in the cable are the same size as the originals? Finer strands could carry electricity better.

Perhaps Volvo overbuilt the original cable, although your original cable failure does not help in thinking that!.

Here is a nice DIY for complete replacement. Note: cables should be crimped, not soldered. I like the use of shrink wrap to keep the elements off, but I wonder what a 'hot' wire will do to the wrap.

--
Keeping it running is better than buying new