You have two choices.  Number one, and the least likely, is that the
heater cores are plugged with junk that came out of the old radiator.
It's possible an acid flush will open it up again, but it's also possible
an acid flush will make anything in the system that is marginal into a
leak.  On the other hand, if you turn the core into a leak, well, you needed
to replace it anyway.

The more likely choice is that there is air in the system and they have
not managed to successfully bleed it all out.  I don't know what year
you have, but I know the older models generally bled pretty effectively
and some of the newer ones may require the system to be drained and
refilled very slowly in sections with the heater valves open.
--scott

try to consider they are foxing you over for money ...

BMW certified mechanics do not do this.

oh geee ... we have to guess now ... we already know that talking to BMW
Head Teacher at Mechanics school in Germany is a waste of time ...

oh common ....

dood .. stop drinking the koolaid.

Tis plugged up .. or there is air lock in the system.

Take the out let hose off with the engine running .. it is always in
circulation as the heater needs block heat the fastests and the thermostate
is closing off the radiator.

No circulation .. plugged up core.

Blow air up the pipes in reverse, or back flush first in reverse flow.

Hunting and plucking like a chicken ... is what dumb foxs do.

Get a better mechanic .. these people are foxed up you are dealing with.
Like Jonestown Koolaid Kristians are foxed up.

They are stuck in their toddler tantrum as a necessary result of child abuse
I am sorry to say .. that is why they have to lie, prevaricate, obfuscate
and tell you a big foxing story.  Check if you are beleiver and can be
easily foxed ... seems you are a bit smarter then that ... as you know where
to find good minds to sort things out a bit better.

sumbuddie wear blind sea