Run, do not walk. Top terminals are connected to eactly the same place in a battery as side terminals (I usually buy batteries that have both so can switch between cars). Now while I would not make that kind of cable switch on a car (side terminals resist corrosion better) electrically, both look identical.
Now the heating of a cable from the alternator usually indicates some kind of short either in the cable or the battery.
If it were here I would start instrumenting things but you are a bit far away so I would suggest a reputable independant shop that specializes in electrics, there is noting magical about it but does take someone who understands such.