Just a little thought that is keeping me awake at night......

In my 2.0FSI the air box has a nice little cover on it.....

Removing it gives the engine a lovely sound but stops using the cold air feed.....

My questions is, as its no longer using the cold air feed will it be drawing in hot air causing less power??? I didnt really notice a difference in power with the cover off but put it back on and there is lag, for example, changing gear the car still seems to be reving..... Its not as "sharp" as it was before....

Any opinions would be very helpful!! Cover on =???? Cover off =?????