how was that battery cable end attached to the cable ?
solder ?
i know it got hot there, but for some reason, the joint doesn't look it was soldered very good. i know my eyeballs aren't the best, but even if it got hot enough to melt the solder, the wire of the cable should at least show some silver in the middle strands.
a while back, i bought a hydraulic cable crimper. i now crimp the cable connection after the cable has been tinned with solder, and the connector has flux in it.
i drill a small 1/8" [or so] hole in the bottom of the connector, then use that hole to allow the solder to wick into the joint, watching the top of the connector, so as to not allow the solder to wick into the cable past the connector end.
i then use marine grade heat shrink with the glue in the "heavy duty" size [which is twice as thick as the regular stuff] to cover the cable/connector area.

please let us know what you find out in that length of cable, as to the place it shorted out.