Water boiling but no showing on the dashboard Bmw 318i

I’m pretty sure If the cooling system looses pressure the coolant will boil, so could it be a leak?

Are you running the manufacturer blend, or straight water?

Bad radiator cap?

I might be crazy but then again Ive only sat in a BMW once but to me it kind of sounds like one of a few things, a bad temp sending unit, a faulty gauge, or huge shot in the dark here the temp sending unit it somewhere in the system in front of the thermostat so the thermostat could be bad not causing it to open (honestly this is usually the cause of 80% of overheating issues) and since the thermostat isnt allowing the coolant to flow on one half of the system you will be reading the right temp because the sending unit is on that side meanwhile on the otherside of the thermostat the blockside the coolant is getting boiling hot, depending on the return system of this car you might see it when you take the cap off, which isnt too recommended since it will probably burst hot coolant on you. Thats just me taking wild shots in the dark.

I know not to long ago on one of the engines at my work the oil cooler sprung a leak and oil got into the cooling system without us knowing it, that oil doesnt mix well at all with coolant and it basically frothed up and lost cooling properties and boiled until it split the radiator wide open.

Might also be worth checking to see if either you have

A) oil in your coolant
Or
B) coolant in your oil

Both would make it appear sort of like a vanilla milkshake depending on how much is mixed where.

Thats pretty much all I know on the issue good luck with it man and hopefully I helped some what

Also if it were me Id find out how hard it is to pull the thermostat and do that, and throw it in a pot of boiling water for five minutes if it doesnt open then theres your problem, its a fairly quick and easy test.

Maybe the sensor is broken so it sends the same siganl all the time or ylu have a leak in your coolant system

E46 is very sensitive to bleeding. It may take a while but just keep at it. Raise the front of the car, turn the heater on max and run the engine until no air comes out of the bleeder. Watch your engine temp though overheating is the Achilles heel of the e46