Faulty temp sensor or paranoid??

Good day all!
The last few days have been very crazy! To start, my check engine
light came for a few minutes, and then went out. Later that day, I did
the stomp on gas pedal five times and got the code..... (1223) Temp
sensor!

Well on the way home, my low coolant code came up and my temp gauge
shot up to almost the red zone, but didn't make into the red. Got
home I pulled my thermostat and found it closed, and after boiling it
found that it would not open. I replaced it, refilled the fluids, and
then found that I sprung a leak on my radiator. Today I replaced
radiator, but still had problems.

No hot air from the heater, and poor circulation, if any. The temp
gauge however showed that all was well. Since I could not get all the
air out of the cooling system, I turned to the water pump. Yep, that
was it. The plastic pump was free spinning. I replace it as well. Now
the temp is hit or miss. At times it won't leave the blue box, other
times it normal. I DON"T TRUST IT. So where do I start? Where is
the temp sensor that feeds the temp gauge?

Also let me say that over the last few months my temp gauge would stay
around the blue box for some time, then at normal when on the highway.
Now I'm afraid that I might have blown a head gasket too. The cooling
system doesn't seam to want to bleed out the air. No I don't have
smoke out the tail pipe, and no signs in the oil. Could this be? Am I
just paranoid?

Sorry for the book, and thanks for any help/advice you can offer.

TF
1995 525i
102K miles