The aux fan will also come on if the radiator outlet temperatures exceed the normal range. Depending on the increasing temps it will 'pulse-up' to almost 95% (possibly more) duty cycle in extreme and urgent case.
Just to be complete this is the precise behavior of the aux fan (assuming we're talking about the M5):
The DME takes the radiator outlet temperature and pushes into the function KL_ELU_TKA (seen below). If the radiator outlet temperature is bad, the DME takes the value from the block sensor, subtracts 10, and pushes that into the function. The output from the function is the duty cycle determined from the coolant temp; the output is held in a register until later.
Next, the DME tries to figure out what the AC's requested duty cycle is. If the compressor is off or the intake air temperature is less than 10ºC, it assumes 0. If there's an error on the IHKA side, the DME assumes 60%. Otherwise the IHKA well send a message over the can-bus (through the instrument cluster) requesting 1 of 16 speeds. The DME takes that number, and uses one of the K_ELU_KKOS[*of16] values. The resulting value is stored in a register.
The two registers are compared, and the DME picks the larger number. So if the speed request due to the coolant temp is higher than the request due to the AC, it will pick that.
Next, the DME checks the intake air temperature. If it is 60ºC or higher, the requested speed will be set 60% unless the previously calculated value is higher than 60%.
Once the requested duty cycle is settled, the DME will calculate a factor based on the vehicle speed. That factor will be multiplied by the requested duty cycle to get the final duty cycle, and this is what the fan speed is set to. In the case of the M5, the factor is 1.0 until the vehicle reaches 120 km/h, and reaches 0 by 150 km/h. Between 120 and 150, the factor will be an interpolated value.
See the image below for the referenced maps / values

The point worth noting is that there is a decent bit of redundancy built into the system. Even if the coolant outlet temperature fails, the aux fan should turn on unless you have multiple sensor failures. Other contemporary BMWs should be similar, but the temperatures, duty cycle values, and speed factors will vary.
Just to be complete this is the precise behavior of the aux fan (assuming we're talking about the M5):
The DME takes the radiator outlet temperature and pushes into the function KL_ELU_TKA (seen below). If the radiator outlet temperature is bad, the DME takes the value from the block sensor, subtracts 10, and pushes that into the function. The output from the function is the duty cycle determined from the coolant temp; the output is held in a register until later.
Next, the DME tries to figure out what the AC's requested duty cycle is. If the compressor is off or the intake air temperature is less than 10ºC, it assumes 0. If there's an error on the IHKA side, the DME assumes 60%. Otherwise the IHKA well send a message over the can-bus (through the instrument cluster) requesting 1 of 16 speeds. The DME takes that number, and uses one of the K_ELU_KKOS[*of16] values. The resulting value is stored in a register.
The two registers are compared, and the DME picks the larger number. So if the speed request due to the coolant temp is higher than the request due to the AC, it will pick that.
Next, the DME checks the intake air temperature. If it is 60ºC or higher, the requested speed will be set 60% unless the previously calculated value is higher than 60%.
Once the requested duty cycle is settled, the DME will calculate a factor based on the vehicle speed. That factor will be multiplied by the requested duty cycle to get the final duty cycle, and this is what the fan speed is set to. In the case of the M5, the factor is 1.0 until the vehicle reaches 120 km/h, and reaches 0 by 150 km/h. Between 120 and 150, the factor will be an interpolated value.
See the image below for the referenced maps / values

The point worth noting is that there is a decent bit of redundancy built into the system. Even if the coolant outlet temperature fails, the aux fan should turn on unless you have multiple sensor failures. Other contemporary BMWs should be similar, but the temperatures, duty cycle values, and speed factors will vary.
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