You can check the secondary air control valve by taking it of the engine (you´ll have to drain the coolant first), and then heating it in a kettle of hot water. If it closes completely it´s ok and you´ll have to check the housing and the pipes leading to it. If it doesn´t close completely, it´s busted. They are available though not cheap (I remeber paying about 110 Euros for one). Checking it is similar to checking a thermostat.
If the valve is ok and the coolant flow towards itis blocked, you are in for a bit of work.
To get mine fixed, I had to drain all coolant, take the secondary coolant pipe (under the intake runners) out, dimantle the housing for the valve, clean and bore out everthing etc. etc. I took the oppportunity to take all external water plumnig apart and replace all and really all hoses at the time (you know it´s allways the little, hard to reach ones that blow right after you´ve changed all the others), changed the water pump, thermos and flushed the system a cuple of times. I came to that after I took a look down the secondary pipe and saw all that corrosion that blocked among other things the entry to the secondary valve.
As usual, a small problem lead to a big job. And after I´d spent a weekend in the garage, I had a fine running engine, great heating (a first) and rock stady temp gauge. But still was left wondering: If thats what the secondary looked like, how will all the little coolant lines inside the engine look?)
Leaves me glad, I no longer own that car
So frankly you should be hoping, your valve is stuck / broken. The alternative is worse. If it is stuck, before spending lots, try to free it with some WD-40 or similar.
No. 8 in this picture is the secondary pipe I was talking about
http://www.realoem.com/bmw/showparts.do?model=7031&mospid=47808&btnr=11_2457&hg=17&fg=05
No 14 is the valve, no 3 is the housing throgh which the coolant flows heating the valve where on my car the entries and exits were blocked, no 12 is the air filter for the valve
http://www.realoem.com/bmw/showparts.do?model=7031&mospid=47808&btnr=11_2456&hg=17&fg=05