Alternator problem?

I was out last weekend and almost got stranded in the middle of the lake when the boat wouldn't start after drifting a little while. When I checked the battery the terminals were super hot. The ground clamp actually started melting some. After cooling for awhile, the boat started up fine and I pulled the fuse on my amp. I just put in a new battery before this happened and it tested good after the incident. The battery is a little smaller than the one I had before. I tested the alternator and it is putting out about 14.7 volts at throttle. That seems a little high but reasonable. We were listening to the stereo so I am wondering if maybe the battery was getting over drawn on. Does anyone know if this could overheat a battery that much? I only have one amp hooked to the battery and it is not too big. I put a second battery in relay this week and will hook the stereo to that. This is far from a new setup but it gets me on the water so age may play some factor. Just looking for any insight on this problem.