I use the reservoir cap to bleed. Both on street and race car(s).

You really need to buy or borrow an AirLift type tool. I paid $75 for a new one.

https://www.amazon.com/OEMTOOLS-2444...nt+refill+tool

I was introduced to these by a diesel truck specialist that told me all air has to be removed from the cooling system in high compression diesel engines or cavitation and vapor bubbles can occur that destroys cylinder walls, but that's another whole story. This tool requires you have an air compressor available as well. How it works is it has two valves and a vacuum gauge and a tube to your new coolant supply. You attach the tool to your reservoir fill and close one valve, the coolant supply, while turning on the other, the engine cooling system and pump fast moving air from the compressor thru a venturi (like an "old fashioned" carburetor pulling fuel from the bowls or a millipore filter from chemistry class). This creates a vacuum in the cooling system removing all of the air from inside hoses, radiator, block, heater core, etc. Once the vacuum gauge reads the proper vacuum, you close the valve to the venturi, wait to see if any air leaks, and if not, you open the second valve that is attached to your new bottle of coolant. The vacuum from inside the system draws the coolant into all of the systems high and low places without any air in the system. It's very clever. I've been using this on the race cars with no or minimal air from the bleed screw once up to temperature.

^^^spend my money^^^

Will this draw coolant out of the system if there is anything left during a flush? Sometimes hard to get at engine and heater core drains when doing a flush.

It will to a degree but that is not it's purpose. You should normally drain as usual. It would be very hard to pull fluid that has pooled at the bottom of the block or radiator tanks that don't deform for instance. Remember that any small amounts of remaining fluid will get sucked out from the vacuum created with the air coming from the compressor. It will get shot out of the hose at a pretty fast rate and will make one heck of a mess.

it is the bleed screw and that is what bmw specifies to open to bleed the system. all e36's have it. and e46's do too. actually is not in just e36's. at least any bmw with an M/S 50/52/54 engine.

i have always done it with the screw rather than cap and have never needed any hose squeezing. pretty simple process.

now....the M10 engine is a different story..:-)

I have this tool if you'd like to borrow it.

-Paddy

Thanks for all the advice and the suggestion on tool (@TurboPooch) and the offer (@Paddy)

I am going to try the bleeding sequence again tomorrow a couple of times and see how it goes. I did take a look at the reservoir, which I had left filled to the top, and it had gone down about halfway.

Will update with results, hopefully good news.

Results
 

I was able to fill up and bleed the system a few times using the methods mentioned here. After that my idling temperature decreased and stabilized to around 207°.

I also did some troubleshooting on the auxiliary electric fan and discovered my low speed relay is bad. The high speed fan works but I never let the temperature get high enough for it turn on. I did test it using my old sensor and a heat gun, it worked fine.

Some notes/observations:

• The scanguage reads from the OBDII so the water temperature I am reading is from the sensor in the engine not at the radiator. Not sure what the differential is but at 227° the high speed fan was not on, I assume my low speed would have come on if it was working. Note that my dash gauge was at 12o clock but around 230ish jumped up. Supposedly the fan temps,at the radiator, are:
  195° low speed on
  210° high speed on

• For testing the Aux fan I shorted the terminals of the radiator sensor plug, you can do this to check both low/high speed. Additionally I plugged in my old sensor, removed from the radiator and used a heat gun which eventually turned on the fan at high speed.

• My upper radiator hose now feels like there is water flowing through it when at temperature BUT it does not feel full. Should the hose be full and hard to squeeze?

Thanks again to all for the help, I plan on some more testing today to make sure the system has no more air in it.

E36 temp gauge is not a real gauge. More like an idiot light. It will stay straight up over a huge temp range.