Just got caught in major rain, no power after I turned car off

Update on my issue. I finally got a chance to get out to the garage tonight and look the wiring over. I started with the battery, the only "issues" I found were the negative cable was a little corroded where it was bolted to the body, and the positive cable had no fuse in it anywhere, I'd feel better adding one. Next I moved onto the alternator wiring and unwrapped most of the harness (which thankfully looked to be done pretty well) all the way to the bulkhead connector, and the only possible issue I found was a nicely soldered connection near the alternator that only had electrical tape protecting it and there was a good bit of moisture trapped in there. I'm planning on cleaning that and putting some heat shrink over it before wrapping it again. Lastly, I moved on to the starter. I didn't notice any issues at all with the starter wiring, but while I was under the car, I saw some wiring laying on the header. I lifted them up, and sure enough the electrical tape and some of the rubber on one wire had melted, leaving the bare wire exposed. It's a plug that goes into the trans (TCI 727), and had 3 wires, here's a pic:



So here's my next question, the wire itself looks fine. It must've just fallen onto the header as I was driving home last, because the melted/bare wire was "clean". Would I be ok to just put some heat shrink over it then rewrap the 3 wires and secure them out of the way, or should I splice a new section of wire in there?

You guys have been a major help. I feel confident working on my own stuff, but I'm pretty green on this older stuff. I think the oldest car I've owned before this was a '93! Lol