Every car manufacturer that has an automatic transmission, has some sort of oil cooler for the transmission. Most all of them have a cooler internal to the radiator.

On MBs, the oil cooler is in the bottom tank of the radiator. The two small lines coming off of the bottom of the radiator are for the transmission. Typically when the oil cooler ruptures coolant goes into the trans fluid. If you find that your transmission fluid is a creamy pink or creamy brown color....well....find another transmission. All auto trans manufacturers use a water based resin to hold the friction material to the clutch plates in the trans, but when water or coolant gets in there it softens all that resin.

But it depends on which has more pressure. The trans cooler circuit typically is 15-30 psi, and the coolant system pressure is typically 15 psi.

Check that trans fluid!!