Using A-pillars as tubes to duct hot engine area/radiator air to the roof?
 

Most A-pillars are hollow, made from stamped and folder sheet metal.
Could you use them to divert hot air from the underhood area to the roof?
Although you might need some electric blowers to pump the air to the roof, IMO the electric power wasted by the blowers will be overcompensated by the hot air effects on the roof boundary layer.

I think you could completely close the engine underbody allowing it to exit only from both behind the front wheels and to the roof.

Eventually the hot air wouldn't require to be pumped by a blower...

I think the A-pillar bottom end is usually welded shut, perhaps a small weep or two if not filled with structural foam.

Would not be much of a fire wall if not sealed off anyway.

2012 Ford Focus chassis cutaway photo
http://media.caranddriver.com/images...s-1280x782.jpg

2010 Audi A8 UK Body Structure | Boron Extrication
http://1.bp.blogspot.com/_0oCrVCzAD9...s-boron-uk.JPG
Larger images in the link:
2010 Audi A8 UK Body Structure | Boron Extrication
http://1.bp.blogspot.com/_0oCrVCzAD9...boron-uhss.jpg
http://4.bp.blogspot.com/_0oCrVCzAD9...e-Frame-lg.jpg

Cutting a hole anywhere near an A-pillar just doesn't seem wise. However, if you can get yourself into a junkyard to see a stripped down wrecked chassis and do an investigative autopsy on it, I would be interested in seeing the results/photos.

Supposing it is structurally feasible, where where it would be more beneficial to place the hot air outlet?
I mean fore/aft windshield header, roof mid section or backlight header
sideways roof center or roof edges

My hollow a-pillar is filled with an airbag... I don't know that you could move enough air through the pillars to make it worth your while. Also, my a-pillars make more noise than any other part of my car at freeway speeds as-is. I can't imagine pumping more air through would be any better.
Not to pee in the punch, but that's my opinion. Ducting the air into the lower pressure areas like the wheel wells would probably be a better use of effort.

The idea has merit, as flow over the roof makes for low pressure, so hot air ducted by the A pillars would be sucked right out.

OTOH, as noted by others, the A pillars already have other jobs to do.

Better to vent the engine bay heat via hood vents, and/or side vents.

I've considered this in my Porsche, by making heat blanket envelopes around heat sources such as the exhaust manifold and turbo, then ducting their heat out through the sidewalls into the wheel bays, known low pressure areas. So, cooling air comes in through the nose stagnation point, flows past the hot manifold. then out the sides or top. Keeps heat from building up in the engine bay, so the intake manifold is not heat-soaked and the engine is fed cold, dense air to burn.

I think looking at theory is great for just generating ideas and concepts, but as a project I see nothing but disappointment ahead - sorry.

Have you calculated the inside of the a typical A-pillar? Is it around 1-2 square inches?

Let's say it's 2-square inches a side, for a total of 4-square inches. How much air volume can you move (ignoring the sizable frictional looses at first), and how much do you need to move to achieve your goals?

Need to increase the velocity of the air to get the volume up, how would you do that (fan at one end)?

Nice idea as an idea, but the reality of the details are going to crush you. The devil is in the details they say, and this is one of those times.

A-pillar duct
 

If you know the volume of air you'll be moving then recalculate the flow velocity at the interior area of the pillars.An ASHRAE Manual would help you calculate the static pressure necessary to move that volume of air against that much wall friction.
And you'd want to know how to deliver the air to the roof at the same velocity of the flow already there,so as not to create a drag-inducing jet.