If the car has a transmission cooler in the side tank of the radiator, yes. This set up is very common.
What vehicle? Most likely to radiator that cools engine coolant, if not then there is a separarte tranny oil cooler.
Most oil cooler lines run from the transmission to the radiator and can easily be seen from under the vehicle.
transmission oil cooler
The automatic transmission oil cooler is built into the radiator. If the oil cooler developes a leak the oil mixes with the engine coolant.
The transmission oil cooler is located in the radiator. A leak that allows oil in the radiator will also allow coolant to enter the transmission doing great harm. Check the transmission , after driving and the oil is hot water vapor will come out of the dip stick tube.
If there are lines coming from the transmission to the radiator, it has a cooler in the radiator. If there are lines from the transmission to an external heat exchanger, that would be an auxiliary cooler.
Take it to an oil and lube shop and have them flush the radiator.
Failed transmission oil cooler, which is part of the radiator.Failed transmission oil cooler, which is part of the radiator.
Usually you get oil in your radiator when you blow a head gasket and oil leaks into your radiator. Blown intake gasket is also possible, as well as a hole in the engine's water jacket (very uncommon). Also, if the vehicle's transmission cooler coil is internal to the radiator, a leak from it may be possible (most tranny coolers are external for this reason).
those 2 lines are oil lines from the automatic transmission to the radiator .these allow for the transmission oil to be cooled
The transmission oil cooler is located inside the radiator. If the transmission oil cooler developes a leak the oil will mix with the engine coolant. Check the transmission fluid. If it looks like a strawberry milk shake the transmission is in trouble. The longer you drive it the more it will cost to fix. Have it towed to a transmission shop asap.
either the transmission oil line to radiater is not tightene or the oil cooler tank at bottom of radiator has a leak