I Like MArine Grade Wire
To expand on what ScEd said about pre-tinned wire, that is what i use. It can be gotten easily at boat supply stores like West Marine. Military spec wire is always tinned and has many small strands as opposed to fewer large strands in lower grade wire.
A likely cause of the heating in your connection is that the wire was bare copper and oxidized - quickly. Bare copper sucks for corrosion and the oxidized wire has a high resistant at the connection. Copper oxide can grow thick enough to be and insulator.
Even though tinning the wire with solder has its drawbacks I think it is better than bare copper. Crimp connections to bare copper have the same corrosion problems.
If you want to make the best repair replace all of the wiring with marine grade tinned wire.