that's the next thing i was going to do... flush the system cause i dont know what coolant or water to coolant ratio the previous owner was using. But does it really matter all that much? could the coolant be losing its effectiveness after 20 min of driving? I'm no expert but the fact that the car maintains its temp for a while and all of a sudden it start to overheat makes me think it can't be the coolant.

What coolant do you recommend BTW?

and yes for the G35