Sounds like overcharging of the battery due to a malfuntioning voltage regulator. The first thing would be to disconnect the battery. WEAR EYE PROTECTION! and face protection. This battery could be launched and very easily explode.
I would not condemn the regulator yet. The previous owner may have overfilled and overcharged a neglected battery so it would start when you came to purchase it.
i also believe the regulator is a Bosch that is a regulator-brush holder assembly that is part of the alternator. The assembly can easliy be replaced and is relatively inexpensive. I rplaced mine on my 190 by crawling under the car in the snow.
1990 190E 2.6
1996 Grand Voyager 3.3
1985 Mustang GT 5.0 5 SPD
1982 Suzuki GS 750T