Since incorrect fluid was used, I think you have more serious issues than a blocked cooler, especially with pressure regulator error. I would probably drop the pan and inspect for debris first. Depending on your findings, a more complete flush or valve body service might be called for. Whatever the case, I would certainly make certain all the foreign fluid was cleaned out.

2002 X5 3.0 285,050 miles (Original transmission fluid)
2004 325i 122,000 miles