I experienced something very similar. I changed the oil recently in the '94 E36. I had been using Mobil 1 10w-40; I put 5w-30 in it, thinking that would be better for the winter weather in this area. No noise until the engine got nice and warm on a recent day when the temperature hit 70 degrees. At idle there was a tap-tap-tap noise coming from the engine. I popped the hood and determined it was coming from the VANOS bulge at the front of the engine. I could FEEL it when I put my hand on it. If I rev'd to +1500 RPM, it went away, apparently as the oil pressure/flow improved.
I checked it out on several other forums, and found a very long discussion about it. I forget where, but I did clip this because it summarizes the problem nicely.
The only clarification I can add is about his statement regarding the "stuck VANOS myth". The VANOS Solenoid can get stuck, this is commonly known, and is a $125 - $150 DIY repair, but the VANOS assembly getting stuck is apparently rare or not possible.
He also says to go 15w-50. I would go to 10w-40 first, 15w-50 is pretty darn thick, it could cause other issues such as poor lubrication at tight tolerance areas (cam and crank bearings), especially on newer and low mileage cars.
Many people do not realize this but vanos is COMPLETELY run on oil pressure alone. If you do not have the proper oil pressure you have no vanos. Imagine the vanos system as a dual oil path way maze. one oil pathway is for when vanos is not engauged, the 2nd is when the vanos is supposed to be engauged. the thing that shifts between the oil passages IS the vanos solenoid, thatts why it is such an essential part of vanos. without it you have no vanos. if the solenoid does not operate 100% vanos will not work properly. Lets say the vanos only has enough force to push change the machanism that changes the oil pathway 50%, well that means only 50% of oil will get into the "vanos on" pathway and thereby reducing pressure greatly which will then in turn only move change the cam timing by 6 degrees (instead of the full 12 as it is supposed to in the mid range).
Another factor that is essential is the oil ITSELF. it is the mechanism by which u push the vanos gears. If you use a really thin oil (aka mobile 1), it flows like water and it does not have the same oil pressure as a much heavier 15w-50 weight oil which is much thicker (think of molasis). the 15w-50 is able to "push" the vanos to the proper specs better b/c it has higher compression & oil pressure characteristics and is much thicker. so your oil is just a crucial aspect as the solenoid or vanos mechanism itself. Thats why you see so many people say "i replaced my vanos but the noise came back!" well duh! u are using the wrong oil or your solenoid is bad.
So basically... if you are have vanos problems here is the order you should replace things...
1) change to a much thicker oil (preferably a 5w40-20w-50, bmw recommends 20w-50 for a reason, but you can do castrol 5w-50 which will work in pretty much every weather condition & bmw recommend castrol anyways).
2) change vanos solenoid
3) then replace vanos unit if necessary (though I have spoken to NUMEROUS BMW master techs and every single one dispelled the "vanos stuck" myth. it simply cannot happen they say, jus thought i'd share that).