You need more than an aux fan
I don't mean to sound flippant, but the aux fan is not your only problem if what you say is true. As a matter of fact, it might be broken but it's probably not responsible for your recent overheats in any way.
First, in sub-freezing temperatures the E39 doesn't need any fans to stay cool. Just by having the hood open, no fans installed, no heat on, it can't get above 70C (I just did this on the weekend trying to bleed).
Second, the main fan, even when not engaged, provides more than enough airflow in these conditions to keep the engine cool. EVEN IF your main fan is failed freewheeling, it'll still move enough air to keep from overheating.
Third, add the heat sink effect from your cabin heater and the situation is even less precarious.
Does your cabin heat work solid or go cold from time to time? What is the condition of your thermostat and water pump? Does the gauge jump around, or smoothly change readings and gradually overheat? What happens if you turn the heat up to full (i.e. set for max temperature and max fan) when it starts to indicate an overheat?
I'd seriously place the aux fan aside in your mind and start checking other things. It's POSSIBLE that it could have kicked in to prevent an overheat depending on what else you've got going on, but the aux fan should not have even been necessary in these kinds of temperatures.
Homer probably had ice&snow blocking the air flow
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Ah! Didn't think of that!
I can't say I've ever had packed snow compromise my cooling before. Again, at freezing temps I'd expect the breeze from the main fan through the kidney grills plus the heater core to be more than enough unless he was doing a hill climb race or something....
Re: Homer probably had ice&snow blocking the air flow
last week i was driving in the snow storm on the highway and after a while my headlights were worthless cause of all the snow buildup on the front. (hids=no heat) I pulled over on the shoulder to clean the headlights real quick and got stuck in some snow so i had to spin the tires for about 30-45 seconds (not constant) and i saw my temp start climbing past 110. At 114c the needle started moving, at 117c it was at the 3/4 line. I [Oops!] a brick and shut it off, i hit the rest button on the climate control and watched the temp drop sooo fast. Anyways i popped the hood and needless to say there was 0 airflow. Driving on the highway in snow clogs up all the air passages. The whole front of my car was wearing a mask of ice and snow. only the fogs lights were clear from their own heat. Headlight washer systems should of been standard on all cars with HIDS. I had to pull over every 10 mins to clean off the headlights.
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