Does anyone have the part number for the main radiator cooling fan for a BMW 1999 328is? Thank you!

In front of the radiator core for the engine cooling the cabin fan is behind the glove box inside the air con module

Cooling fan does need to be working. It could be a bad fan or the cooling fan sensor.

there is 3 relays on your car

It is not your ps pump that is staying on, it is the ps pump COOLING FAN located below the pump. On 2001-05 Minis, this fan is wired directly into the wiring of the main radiator cooling fan, which has two speeds, low and high. When the engine compartment temperature reaches a certain level, the main radiator fan is supposed to come on, and since the ps cooling fan is also wired into that, it is supposed to also come on. But, that low fan speed is achieved by routing power to a resistor, located at the top back of the radiator on passenger side, that cuts the power down. This resistor is highly prone to corrosion and failure. When that happens, neither the main radiator cooling fan nor the ps pump cooling fan can come on UNTIL the engine compartment temperature reaches an alarming level, which switches through a relay power directly to the fans, by-passing the resistor. By then both fans are attempting to bring the temperature back down to a safe level. Then, if you turn your engine off before the temperature reaches the lower threshold so that the fans are still running, the ps pump cooling fan will just keep right on running, as there will be no relay signal given to turn it off, and your battery will be drained.
To fix this, the resistor either needs to be replaced, or, the resistor can simply be removed and the contacts jumped. This last fix will mean that when the lower temperature threshold is reached, the main radiator cooling fan will come on at full speed, and the ps pump cooling fan will also come on. After my ps pump failed due to fan failure, I did this to my '03 Mini, and have run it for years this way. No more ps pump problems. You do need to make sure you keep the fan clear of debris and freely turning, or you could have bigger problems, like a fire, since the wires will get very hot sending power to the fan motor when the fan is bound up with the motor not turning. A blown fuse will often be the first indication of a fan bound up.

that has 2 sensors one ac and one cooling should b a sensor on shroud near cooling fan

the cooling fan fuse is located in the main fuse panel,location of which should be in your owners manual if you have one if not call the dealer and ask.it could be the cooling fan motor itself not working or the cooling fan relay.to check the cooling fan if you disconnect the plug on the back of the motor and feed direct power and ground to the terminals of the motor.if the fan starts to work then it is okay.to change the cooling fan it is a job for a shop to do as it entails alot parts removal to get to the fan itself

no the fan in front of the radiator is actully in front of the a/c condensor and serves to pull are across it for the a/c system. no fan on the motor will over heat the engine

Sounds like a cooling fan are not turning on. Assuming you have an electric cooling fan. It could be something simple like a fuse or a relay which is stopping the fans from working, or it could be something as bad as the motor burning out on the fan.

You may need to replace your gaskets and seals now. also, get your block checked to make sure its okay...