Would the air get that hot when passing the radiator at speed? maybe a few degrees possibly worse when stationary but not that much, surely?
All air is managed in a GT and QP.
All frontal air goes ether through center which is enclosed conveyor to the radiator (just in-front there are two scoops for air filters) then you have the side ducting bleeds trough the wheel arches (brake cooling etc) on a F1 it goes against the oil reservoir,
This makes your radiator conveyor a high pressure area (full incoming air speed car speed + wind condition) slowed down by restriction of the radiator, (hence that over pressure enters the air-boxes cold and at incrementally more pressure)
Secondary restriction that a MC Stradale some what resolves is the hot air trapped in the engine bay can't exit easily and builds up back pressure, the hood vents in a MC allow that to escape.
The effectiveness of a ducted intake and exit from radiator is huge just check any race car or modern supercar they all utilize the effect i forgot the basic calculation i recall it's 30% efficiency gain in a directly ducted setup (think GT40, Lotus etc)