Your dual aux radiators, by model, are:
228i = both are water
M235i = passenger side is water, driver's side is oil
I have NO IDEA if this has changed for the B-series engines. Let's assume that they are the same.
During the time I was researching
this issue way back in 2015 on behalf of my car and everyone else's, a buddy dug up information buried deep in the tech manual for the N20 on target operating temps. What we found was very interesting:
In the four driving modes that our cars have, the target operating temperature goes down an average of 5-7 degrees F for every mode change from Eco Pro to Sport +.
No, 'down' is not a typo. Basically, our engines are designed to run
cooler as the engine mode selected becomes more sport-oriented. This is likely to offset greater loads on the engine and is likely the main reason cars with THP (an option on the 228i, and standard on the M235i) in the U.S. get the second aux radiator -- and why any convertible, no matter which model and market, has only one aux radiator.
I've observed the operating temp differences with the P3Cars gauge I have in my 228i. The difference is less pronounced in oil temps vs. water temps, but it's there. I can only assume that the N55/Bxx engine in the M235/M240 needs extra oil cooling to achieve those BMW operating temp targets.