Is it possible to add a 3rd party temp sensor to a car's existing cooling system by connecting it to the thermostat housing? ?

Everything you said is meaningless horseshit.  Just go away and stay off.

The electric fan temp sensors are usually mounted on the brace or hardware that holds the fan in place behind the radiator. This measures the coolant temperature in the radiator and not the temperature of the coolant coming out of the engine block by the thermostat. If you did it your way, the fans would run non stop once the thermostat opened and run until the engine cooled off after parking it.  

I don't know anything about a fan being electronic.  It's just an electric fan, as compared to being a belt-driven mechanical fan. 

P.S.  You need to think this out better.  Hot engine coolant is on the engine side of the thermostat.  You are talking about the thermostat housing which is the radiator side of the thermostat. 

The sensor that turns on the fan needs to monitor which temperature?  If the thermostat is closed (purposely or accidentally) then engine heat stays in the engine. 

I'd just use the factory fan.  It will, however, make more wear on your water pump bearings.

Possible, yes. Worth the effort and expense - no. If you wan't noticeably better performance, either do a major overhaul on your engine and drive-train or get a different car.

You are definitely not knowing more than BMW Research & Development guys when they designed this car(you definitely do not have the $ capital they have plus the numerous cars they have at their disposal.   You have 1 car.      

.  You want to mess with their system? Meaning you got to take to them to fix it right again. Beemer owners usually have lots of cash...because they is so costly.

.  Beemers are pigs on fuel.  For more power you get lower MPG.    Fan has nothing to do with the throttle response.

It is cheaper if you were doing it on "Buddies car"  If it blows up or drives like a tank, it is not YOUR car. So you shrug your shoulders and leave...and go visit that Blonde chick.

Do it wearing a mask...so kinky.

Your car has a fan clutch.  It disengages the fan at a certain engine temperature.  There is NOT much to be gained putting an electric cooing fan. 

Leave the car alone.  The transmission will break anytime soon and any "improvements" that you make will just be a waste of money.

I wouldn't modify a BMW. You're lucky the damn thing is running as it is. An electric radiator fan is not going to increase your MPG and I seriously doubt you'll have any better throttle response. Put a cat back exhaust system on the car. That will give you 25 more HP and maybe an extra mile per gallon.

just fix the mechanical fan you will get bugger all gains you aren't smarter than the BMW engineers the designed the car. the electrical system wont have a spare 40 amps to run the fan . 

if the engine is hot when you turn it off and the fan continues to spin its rooted.

Possible?  Sure...

Keep in mind though that the fan in your Beemer has a fan clutch.  It engages when necessary as opposed to being directly connected to the engine all the time. I don't think the work is worth the effort.