[MrMCar]

It's easy:

Open up the radiator (expansion tank) cap half way. Squeeze the upper hose with all you've got. At the same time tighten the cap. Now your cooling system is under slight vacuum.
Have everything at the READY.

Pop the sensor out and have the new one slightly lubed. Make sure the old O Ring comes out, have a pick ready if not. Pop the new sensor in and make sure it clicks. Give it a tug to be sure it's ALL the way in. Reconnect the electrical connector.
Open up the cap and top off.

Loss should be minimal.

 

[MrMCar]

If you've only lost a very small amount (above) a top off will be fine.
Folks run into issues when the coolant level drops below the minimum mark.

 

[MrMCar]

Sorry to be a pain my car is an automatic and has been trying to overheat in heavy traffic soon as I'm moving again it's fine I've got no coolant leaks etc. My electric fan isn't coming on and I did have a sensor fault code so I've just replaced it. My air con isn't gassed at the minute it's empty, does my air con need to be filled for it to activate the electric fan or should the fan come on regardless once I press the AC button.

E46 Electric Fan Guide 2019.pdf

drive.google.com

 

[MrMCar]

Sorry to be a pain my car is an automatic and has been trying to overheat in heavy traffic soon as I'm moving again it's fine I've got no coolant leaks etc. My electric fan isn't coming on and I did have a sensor fault code so I've just replaced it. My air con isn't gassed at the minute it's empty, does my air con need to be filled for it to activate the electric fan or should the fan come on regardless once I press the AC button.

Given that your car is an automatic AND the coolant temps are fine when motoring (air moving through radiator) this is a classic sign of a worn out fan clutch.
The fan clutch is supposed to start locking when there's NOT enough air flowing through the radiator; you sitting in traffic. That's what it's there for.
On a automatic, the mechanical fan IS THE PRIMARY cooling device.

 

[MrMCar]

Spinning yes, but with verve? Perform a rolled up newspaper test the second the needle starts heading north of straight up.
BE READY to turn the heat on, as a supplemental cooling device.

 

[MrMCar]

Here:

 

[MrMCar]

This means it sucked air into the system when the upper hose expanded. Depending on how much air was sucked in (how much the upper hose was compressed), it might need to be bled the air out.
You don't need to compress the upper hose at all if this is done on the cool morning as the system is slightly under vacuum pressure -- just don't touch the tank cap.

I've NEVER had air in the above method. In fact you can see the liquid right there in the cavity.

If it did suck in enough air to warrant a re bleed, there would be coolant on the ground. After it chugged out, tantamount to an upside down gas can

 

[MrMCar]

Let's look at how many have issues with properly bleeding the cooling system, quite a few....
Now if the above is done properly and quickly, no cooling system bleeding becomes necessary.

However if everyone performed a system bleeding, I'd bet that 50% of the folks would create an issue that did NOT previously exist. This is an unwanted outcome.

 

[MrMCar]

I'm not talking physics here. I'm sharing what has worked for me for over decades.
If you're uncomfortable with it, don't do it. Simple.

 

[MrMCar]

Someone needs to calculate the fluid mechanics of coolant/air through the narrow passages of the radiator. I'm fairly certain that is like sucking water through a narrow straw. What is the negative pressure on a fully collapse upper hose? I don't know what the exact answer is.

I've calculated that I've been doing this for over 30 years (I've worked on other cars before the E46 came about) I haven't had a single issue.

That's the mechanics of a technician.

 

[MrMCar]

If OP followed Mr.M suggestion then the hose was not just slightly collapsed but it was squeezed the last drop of ...out .So the vacuum is much stronger than the slightly collapse hose from the cold temp in the morning.

The air probably not traveling through the lower hose with a closed Tstat, but it moves through the radiator and up to the upper hose.

Could you, would you open up a radiator cap and squeeze the hose if the engine was hot enough for the thermostat to be "open"???