The warm air intake on the airbox has got nothing to do with cold starts.
It works on inlet air temperature, if the air going through the inlet below a certain temperature then the flap starts to open until the normal intake is closed, and the intake to the exhaust manifold shroud is open, so hot air drawn in to lower the intake air temperature.
I would drill the air box front and wing side only, and put in a k&n panel filter. Also remove the trumpet inside the airbox as said above. You can also remove and plug the vacuum lines that operate the hot air flap, so it doesn't open at all, as also stated above its not really needed in this climate.