There is only one expansion valve and evaporator - the cold air gets ducted to the back from the front, so I think you can assume the main loop of the AC system is working fine. I think you are left to consider '

1) hot air is being introduced into the front (heater valve, etc) - I don't know why this would take so long - unless your 20-minute delay is how long it takes your car to warm up (but that seems too long)

2) the flaps and actuators directing cold air are somehow failing/getting mixed up, etc., after some period of time

3) the fan in the front is failing or slowing down (weird failure mode of the fan resistor?), allowing more hot air/outside air to leak into the front vents. The back does have its own blower fan. Do you have the same problem when you set the fan speed manually and set the return air (recirculate or fresh air) selector manually?

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles