HKs FD3s

so i've been reading up cold intake vs open (hot) intake.

from what i gather cold intake is better bec of 2 reasons (assuming stock ic):
(i) draws in cold air from outside and not engine bay leaving little air for the highly inefficient ic; and
(ii) turbo spools up a lot quicker (as evident with the increase in boost).

then again, with the open intake, if it sucks in hot air from the engine bay does it mean the ic would get cooler air?? (or simply less air?). also, bec the open intake sucks in hot air - there wouldn't be as big an increase in boost... therefore, is it safe to say when running an fd w/o ecu and just dp and catback, open intake is the better option?

i'm sure it may seem stupid to many of u out there, but no harm asking right?

cheers
HK