The PS cooling fan is not connected to the EHPS pump and is independent of it. It is operated by the stage 2 cooling circuit for the engine cooling (shares the same power relay). This is initiated once the engine temp reaches 122C.
The EHPS pump has its own controlling electronics which can be accessed via the EMS with an OBD2 connection and diagnostic software, it is independent of the Power Steering Cooling Fan. The EHPS pump has 4 fault codes that can be stored in the EMS memory. When the EHPS pump reaches an Overheat condition it reduces to 80% capacity. Once it reaches 100% temp threshold it will shut down to protect its electronics.
Memory Faults Stored:
Power Supply Fault
Electric motor fault
Fault caused by excess temp
Control module fault (the pumps control module)
CHF 11s power steering fluid has an operating temp of -40C - 130+C, this being said, if the cooling fan initiates at 122C it should cool the pump body down before 130C is reached.
If the pumps control circuit is damaged by heat or a build up of dust on the circuitry (mentioned in earlier posts) then the pump is shot, also check if there is damage to the wiring harness to the pump.
Hopefully this clears up a lot of confusion between the operation of the EHPS pump and the Power Steering Cooling Fan operation as I've seen a lot of confusion and red herrings on this subject over several forums and its taken me 2 months to fathom all of this out.
I've just replaced my EHPS pump on a 2002 R50 and hopefully I have no further issues. A point to consider as mentioned in as previous post on this forum, a pump removal and strip down and clean at around 20000 miles (from memory) as preventive maintenance of the pump motor may help it to last longer depending on the warranty period of your new pump.
Hope this is of some help.