I have a cold air box in conjunction with my cowl induction
and 351 Cubic inch police interceptor air filter. You can see it at the Honda/Acura meet at Phillipe Park on Sunday.
A cold air box definitely keeps the heat out of your intake.
Cold air produces more power when the gas is ignited in the engine.
I build ducting and cold air boxes, and design them in a different manner than the "bolt-on" trendy stuff, however............. -Bob