75% of the time after work is done & you're overheating, it's because someone didn't plug the connector in on the powersteering pump. The other 25% of the time the thermostat is installed incorrectly, or is faulty. Usually, if a P/S fan doesn't spin fast, it's because the connector has simply been unplugged
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The radiator fan is powered by the power steering pump. You loose fluid, you loose the fan. . It's a fluid motor, it slips like crazy - don't worry about it.
The fan has 2 speeds low and high.
If you'll look on top of the power steering pump there is an extra outlet / inlet with an electrical plug by them.
The electrical plug is a solenoid controlled by the cooling fan ECU. The ECU opens the solenoid all the way & the fan spins fast..
The only problem is if the electrical connector that plugs into the top of the power steering pump is not connected. Which is common when people are changing the P/S belt.
You can check that the fan/fan computer/high-pressure relay are working correctly by opening the Diagnostic port in the engine bay & bridging E1 & OP1. Use paper clip or jumper test wire. This should give more fluid to the fan, causing it to spin faster.
In the Diagnostic port, bridge E1 & OP1 & the fan will spin at high speed.