afpojdspo? Sorry, I'm not a man of letters!
I honestly don't know how the trans. cooling therm affects the rest of the system, but seem to recall an issue with trans. therm causing issue with cooling system. You're getting more heat into car because of trans and need to get it out...but it would surprise me if the aux fan failing is enough to cause an overheat...but then again, as we know, our car is one of fine balance...damn it! lol
Be dispassionate about diagnosing your system...just like a mechanic. One-by-one, easy/cheap, to difficult/expensive, and if your attempt doesn't work, just go wider in your replacing of random stuff. Still don't know if therm is aftermarket one or not...if it is, it 'could' be as simple as that. It 'could' be just the cap, but that's doubtful.
Your fan hadn't worked for a while, I guess, so either you've been lucky in your driving patterns, or something else has failed.
Also, on the 'boiling' and your mix: not so sure the mix could be that far off, as that'd be kind of odd...even here. When pressure is released, though, much gas that was dissolved will come out of solution. Why? PV=nRT
If you meant because steam was pouring out of system and thought it was boiling...that would just be because system was really hot and under pressure.
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Mangofy your E46!