Cause of leisure battery overheating?

Upon leaving site last Saturday, when I opened the leisure battery compartment on my caravan to disconnect the hook-up cable (following the correct procedure), I realised that the battery was extremely hot. It wasn't smelly or bulging but as it was so hot, I worried about it exploding and so disconnected it putting it somewhere that it could cool down. As I disconnected the hook-up power, the caravan meter dropped from 13v to 10.5 v. Once home 6 hours later, the battery was still slightly warm and the voltage (using my multi-meter) was only 5.5v so I know I need to replace the battery. However I don't know if it overheated because:

1. The battery (which is at least 4.5 years old) has just died of old age
2. The battery has been overcharged by the charger (between the hook-up input and the battery)
3. The battery has been overcharged by the solar panel (via the panel controller (CMP12))
4. Something else

I've had no other battery/electrical problems with the same set-up since buying the caravan 4.5 years ago.

Given the urgency of the situation on site (& my ignorance about the order of disconnecting/connecting solar panel controllers), I didn't disconnect the solar panel from its CMP12 controller until today (Monday).

I reconnected my hook-up lead at home (with battery disconnected) and measured the voltage across the leads that come from the charger - 13.5v (which seems ok). I don't know if it was useful to measure the current with battery disconnected but it was 0.5mA. This leads me to think that option 2 isn't the problem.

After disconnecting the solar panel from its CMP12 controller today, the panel (in sunshine) measured 21.5 volts across the solar panel connections (in fact it measured the same when the panel and CMP12 were connected). I measured 0.82A across the solar panel connections.

With the solar panel connected to the CMP12 panel controller (but with the battery still not connected to anything), the output from the controller to the battery leads is the same as the input to the controller (i.e 21.5v 0.82A). I'm wondering if the CMP12 is now broken (either because it was anyway and thus overcharged the battery, or because I disconnected the battery from the controller before disconnecting the solar panel?

I clearly need a new battery but don't want to break that one by overcharging it.

Any advice gratefully received. Thanks in anticipation