Battery overheating on shore power usually means battery overcharging.
But it can also mean other things (Example shorted cell)
Measure the voltage at the battery both when overheating and again, 1/2 hour after you either unplug from shore power or turn off the breaker that feeds the converter.
Page 2: One of the things I learned this week the a danger of SEALED lead acid batteries (Full name Valve Regulated Sealed Lead Acid) this inlucides AGM and Maintenance free designs, in fact all Maintennace free designs (Of which AGM and GEL are sub sets).
In normal battery operation water is converted into it's elements Oxygen and Hydrogen, and in SEALED designs these are re-combined internally.. This, generates heat. Vented liquid filled (Flooded wet cells) the gasses escape and likely re-combine later under other conditions. But the heat is NOT confined to the battery housing.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times