Well I suppose it's either the battery or the alternator/reg as we know.
I'd be slanting towards the battery - my theory's a bit hazy, but I wonder if a plate or two have buckled and are shorting with others, reducing the battery capacity, i.e. it may be accepting a max of 10v for example, the diff between 14v and 10v is greater, causing the battery to get hot.

You could try putting it on a battery charger for a few hours, and see if it gets hot and may start to boil electrolyte, if its does at least it rules out the alternator.
Perhaps run your BA battery in the lancer (if it will fit) and see if the same problem arises. Just touch test it often, obviously for it to spew electrolyte, it will get pretty hot.
Voltage doesn't always show the whole picture - older cars used to run ammeters, certainly would be handy in this situation, would show what the alternator/reg is doing.