At one extreme you could imagine a world in which the engine sucked in each molecule from the engine bay before taking in another one from the outside world. That means that after 13s the engine bay would be completely cleaned of "warm" air and replaced with ambient air from outside. Most of this air won't then be in contact with anything much warmer than ambient (air is a moderately good insulator) so won't heat up much and in another 13s or so will have been injested by the engine anyway.
At the other extreme you could imagine that the engine intake makes its own duct of some sort because the air will naturally flow from the points of ingress to the point of low vacuum (of course there will be air moving in all directions and eddies in the corners where air doesn't flow naturally, but more-or-less it will be flowing towards the intake). You could imagine this path being a volume of perhaps 100l, so it'll be injested in just 1s.
At speed the vaccum left behind the car above the rear deck pulls air through the holes in the undertray (very cold air usually) and the side pods, so the engine bay temps are much cooler than you think anyway. We once put bits of string on the side pods and observed from a second car - there is plenty of air flow into them.
The boot is not a good indicator as (a) it's cooked by the exhaust and (b) it's more-or-less sealed so no airflow through it.
So without an air hose the only time the air the engine injests is going to be much more than ambient is when you're not using any RPM and you are travelling slowly, e.g. in traffic or cruising in a <40 mph zone, or when transiting from such pootling to full throttle.
On track and spirited A/B road driving this just isn't going to be an issue; for boy racers burning off from the lights, it might be
On a dyno the engine gets about as hot as it can because it's relying purely on water cooling with no airflow through the engine bay due to speed (though there is still the flow due to engine injestion, obviously). On a R/R you would be able to measure the worst case effect of engine bay heating on full power by running first with and then without an air duct, but without using any fans to force air into the side pods/engine bay. In one case you'll be running on mostly ambient, in the other you'll be running on whatever blend of heated air the bay feeds the intake.
Another interesting measurement would be a thermometer placed in front of the air intake and wired up to a remote readout so you can observe intake temperature while running (or just tap off the one that's already fitted to the intake).
Cheers,
Robin
