Enough air is FAR more important than 'cold' air

This is another thing I see all too often, and that's people obsessing over creating a cold air feed for their turbocharged engine, and usually at the same time neglecting other things that have a far bigger effect on performance.
It's all well and good having a fully enclosed cold air feed to your turbo, but if it's too small, and in most instances it is, it doesn't matter how cold the air is, your car will perform worse in every way than if you had a totally nonrestrictive air feed, even if it sucked in full engine bay temp air.

While a cold air feed is a bonus on a turbo car, it's really, truly, not a big deal, and not something I'd exchange for even the slightest restriction. Unlike with N/A, the air goes through the turbo compressor, heating it up hugely, regardless of how cool it is, and then, providing you've got a good setup, it goes through a highly efficient intercooler and exits at a very low temp indeed; way below 40degC. 
If 1deg increase in compressor inlet temp equaled 1deg increase in intercooler outlet temp, it would seem more useful, but unfortunately it doesn't work like that.

Also, while under-bonnet air temps are high when static or on an engine dyno, in the real world, ie when you're flying down the road under full load, the engine bay air is moving so fast that any one portion of air is under the bonnet for such a tiny amount of time they don't get a chance to get hot, so, well, they're not...
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Finally, and perhaps most importantly, is any restriction. While you can't see or feel it until it's SO bad it's actually sucking your inlet pipe shut, trust me, fit a vac gauge to 80% of turbo inlet pipes and there will be a restriction. Any restriction at all decreases compressor efficiency, which in turn increases compressor outlet temps, totally negating the usefulness of any 'cold air feed', not to mention needing more 'power' on the turbine side to spin the compressor, which will increase pre-turbine backpressure, which then is bad for temps, performance, and reliability.

BASICALLY, while cold air is always, always good, it comes a big big big second place behind having a massive and nonrestrictive air feed.
​Huge air filters and 4in inlet pipes for all!