Obviously a valve or gate of some sort would be involved to regulate the temp and not just a simple “always open” solution.
Then you run the risk (in a weapons bay, it wouldn’t be a risk – it would sure as hell be an eventuality) of introducing stagnant pockets of air which quickly become local hotspots.
Its a problem I’m painfully aware of at the moment (not on F-35 before anyone asks) and fixes unfortunately aren’t often clean and simple.
What would probably be needed (for F-35) is a liquid cooling solution; where the components introducing most heat to the bay are glycol cooled with the refrigerant going to a liquid-air heat exchanger which can then be fed via your small duct, with air forced through the HX as it goes down the duct. The valve can then control massflow rate down the duct and it can only go through the HX so no possibility for stagnant zones.
With proper duct design (Meredith effect), drag effects can be zero, if not actually providing thrust at higher machs.
Of course it all adds extra weight, needs electrical power and at low altitude in higher temp climates it may not be that effective without introducing a proper vapour-compression cycle. But that needs even more weight and power.
Urgh.
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