the radiator cap didn't blow, the soft rubbery cap on the overflow tank popped off and released the water.
That depends upon how
blow is defined. If a Brick radiator cap's pressure valve becomes defective, pressure in the radiator decreases causing the temperature of the coolant to increase. Boiling coolant and hot vapor is then directed into the coolant reservoir where pressure increases until it blows coolant out of the
reservoir. It is possible that a defective radiator cap could be
one valid cause of your boil-over problem, as frankenduck indicated.
The radiator fan and thermostat work in tandem to keep the engine at an optimal operating temperature. When a radiator fan kicks on, it's just keeping the coolant at the optimal temperature. It isn't a sign of a system defect. If the fan's operation fails to stabilize an increasing engine temperature, the instrument cluster warning light is lit.
Your Brick could have a defective temperature sensing module, but it could just as easily have a blown warning light bulb or a defective coolant temperature sensor. The sensor has two circuits, one is connected to the fuel injection control unit and one feeds the temperature sensing module. Test each possible source.
View the flow chart and the troubleshooting guide found using a link at the bottom of the
Service Manual page. The guide explains most of your Brick's systems and how they interact. Also,
this BMW manual gives a detailed explanation of the ignition and fuel injection control units' interaction with other engine components. Many other references are available at this site.