On my M103 I had one bad fan and it didn't get unusually hot like yours. I expect its the engine fan. The electric fans can't cool an engine by themselves, I've been able to tell right away when the engine fan stops working.
I did fix my aux electric fan. One of the brushes stuck. I just had to take it out and apart and un-stick it. Your's is slow so it just needs cleaning/lubing. On my 190e the front bumper had to come off. If its the same on the 300e, take the temperature sensor off first before you drop the bumper, its in the licence plate frame.