Fan
I have not studied this particular issue nor have I done any tests but I don't think that the fan would take care of the problem. To me, it seems that there is just too much space and heat between the cockpit air vents and the a/C box. You would almost need one of those big box shop air conditioning units sitting in front of your grill to deal with all of that hot air. Personally, I wouldn't waste the time and money with your project that will also pull quite a few amps from the system when it is on. Oh yes, if you are worried about radiator protection, read the thread on this topic to see what several of us have done. I used a large piece of expanded aluminum and painted it black. I have not noticed that I have stopped any stones but I killed an entire squadron of grasshoppers when they wanted to fly into my radiator.
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