Sounds like your previous owner may have installed an el cheapo Middle Kingdom sourced radiator.

Get an OEM replacement - Behr (Hella) - get the European one not the Asian knock off.

The transmission oil cooler is a part of the radiator itself.

Make sure you use genuine M.B. coolant or Zerox G05

Using only water in these M.B.'s will deteriorate the individual compnents of the cooling system very quickly