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Hi booploops and welcome.
Your idea has some merit but, depending on your vehicle, there are easier ways to pick up warm air.
What many do (me included) is to draw air from behind the exhaust manifold heat shield.
The benefits of doing it this way are:
The exhaust manifold heats up quicker than the cooling system, so you have warm air to help while the engine is warming up.
Once the cooling system thermostat is open, the air is preheated passing through the radiator, then warmed up further by proximity to the hot exhaust. This may (or not) result in warmer air for the intake.
You don't have to cut a 2" hole in your firewall.
My June (mid winter) average last year, just sucking air from behind the radiator was 41.2mpg. This year's June average was 42mpg sucking from the manifold, despite colder weather.
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