Alternator wire from alternator to starter smoking hot broke

Installed a remanufactured alternator. Wire between alternator to starter started to smoked and broke. Used a piece of wire and added a splice to replace broken wire. The replacement wire was just twisted together and taped with electrical tape. Alternator appears to be charging the battery at approximately 13.5 volts but had to shut it down because wire between alternator and starter was starting to smoke. Also the end of the battery cables were being changed and they crossed touch the cable to the negative and positive battery posts and caused a spark before connecting the battery. Could this caused the wire between alt and starter to get very hot? Or something with alternator? Does the wire between the alternator and starter have a fuse? I didn't see anything that looked like a fuse.
thanks