e39 aux fan temp sensor

[Xero]

So my car has been having overheating problems, and I know it all started with the auxiliary fan malfunctioning sometime during last summer, it would kick on full blast for a few seconds and it would be ridiculously loud then just turn off and never come on, later on I noticed overheating and eventually had to replace the waterpump (apparently the blade had cracked or something, probably from the extra heat), but the aux fan was never fixed, I didn't realize this until later and I have done the tests in the many guides and have determined the fan itself turns on fine, just the temperature sensor is faulty. Anyone know where I can get one of these at? I'm trying to buy one online if possible.

I think there must be a leak in the cooling system as well, because the car still overheats and its freezing outside, and I've just been topping off the fluid and this will solve the problem for a couple of weeks...although I'm wondering if having the aux fan not working could be potentially causing this issue by maybe the temperature getting slightly too hot despite how cold it is outside...it seems when I have the heater on in the car and i'm going up a hill or something the heat starts coming out way hotter, and of course the aux fan isn't kicking on, so if my heater hadn't been on, i'm supposing the engine and cooling system would be receiving a lot of that extra heat..

another issue i've had recently is that the car has been having a little trouble starting in the cold, I usually have to give it some gas or else it will either not start, or it will start but some cylinders are definitely misfiring...until i give it some gas...then everything is fine. Once the engine is warmed up, everything works as you'd expect. I had a tuneup done fairly recently, so it's got all new spark plugs and air filters and all that....any ideas what might be the issue? I never had trouble starting in the cold before, and it's been a lot colder and still started fine. Should also probably note that the check engine light has been going on/off for a while now...tends to go off when I have less gas in the car...so I was thinking it was that issue with the gas cap, it had stayed off for a while but just came on again about a week ago...

my worst fear is a blown head gasket, although I never ran the car with the temperature in the red for very long (I always turned on my heater full blast and it was usually back to normal within seconds, there was only one time it was red for more than a few seconds and I had the heater on full blast the entire time, the car wasn't moving so I can't imagine the engine was putting out that much heat, was stuck in stop/go traffic on a highway, ugh) and my mechanic didn't think it was anything serious...it's been months since i had the waterpump replaced and that was the only time the car had serious overheating issues. I sure would like to rule out this possibility, the missing fluids could certainly be a symptom but then again tons of things can cause that....I haven't noticed any excessive white smoke or anything but with the temperature as cold as it is, even breathing makes white smoke...sooo) plus the engine otherwise seems to run excellent...I do notice a funny smell sometimes when I come to a stop, although I really don't know if that can possibly be related, I always figured I was just smelling the brakes or something.