1.8GTI Auxiliary Air Valve Adjustment

My 1983 1.8GTI starts from cold with no problem and runs fine. It starts and runs fine whether hot, warm or cold but as it starts to warm up the idle speed drops and becomes lumpy. I've done a few checks and come to the conclusion it's the auxiliary air valve.
When the engine is cold it starts almost immediately without any throttle needed and ticks over at around 1000 rpm. If I rev the engine the revs drop to below 1000 but come back up and settle at 1000. After about a minute the revs start to drop to around 600- 700 rpm and if I rev it the engine nearly cuts out but then settles at 600-700 rpm.
When the engine is stone cold idling at 1000 rpm, if I squeeze the aav pipe the idle drops but doesn't stall. Once it starts to idle at the lower speeds, when I squeeze the aav pipe it makes no difference to the idle which is why I believe the aav to be faulty.
When the engine warms up it idles happily at 950 rpm.
Can the aav be adjusted to allow more air through for longer at cold temperatures? There is  a screw with a lock nut on it but I can't turn it while it's bolted to the car. Or am I better off just replacing it?
Thanks.
 

No, but its nothing to do with the AAV, rather the mixture needs checking/adjusting.

Thanks for the reply. Not sure it's the mixture that's wrong as the C/O when warm is 1.49 and the car runs absolutely fine when engine is hot or stone cold. It's also not a problem in the summer when the weather is warmer it's only a winter problem when the engine has started to warm up. It's also a problem that's been there over the last three winters.

Both of the Mk1's I've had have run better with the CO set at between 2% and 2.5%, they still did at leasrt 35mpg around the back roads here and the plugs were a nice healthy colour, you could try it and of course super unleaded petrol.
By your description of the way your AAv is behaving I would say it was okay but it is possible that it is not the right one for the car, they all look the same but behave differently.

Thanks for the help.

A small update:
I found a loose jubilee clip on one of the hoses on the AAV which I've now tightnened up. It seems to have improved the cold running quite a bit. I need to check the CO again but that's anther job for another day!

I'll post any updates.