The engine is cooled by water, and that water is cooled by the air flowing over the radiator.
So you don't want more air going into the engine bay to cool the engine, you want more air going through the radiator to cool the water to cool the engine.
The best way to do that is by ensuring the air coming into the engine bay has nowhere to go except through your radiator - this is why people spend a good bit of time making sure any gaps around the radiator are sealed, and creating ducts that ensure the air has nowhere to go except straight through the radiator. The factory undertray will assist with the latter. See this thread for example:
http://mx5cartalk.com/forum/viewtopic.php?f=30&t=71173&p=874025#p874025I wouldn't worry about under-bonnet temperatures (or the perception of under-bonnet temperatures) - what I would worry about is the water temp, the oil temp, and whether your air intake has a good source of (relatively) cold air.
It seems like with your current intake that's a resounding yes to the last question, so no issues there.
The other questions to answer then, are your water and oil temps ok, and you've not mentioned anything indicating either of those is too high.
From what I know about your car on this thread, I would be incredibly surprised if you had issues with either of those things.
The feeling of radiant heat from your exhaust manifold is not an indication of anything other than the fact that hot gasses flow through there (a good thing - that's what it's there for).
2004 SE - stock ECU, stock engine, BEGi intake, FMIC, BC Racing 10/6, 15x8s, 225/45 NT-01s
Barbagallo long: 70.488
Barbagallo short: 58.999