Thanks for that.
I saw a short article in Popular Science/Mechanix years ago about a Porsche race car that had a similar installation. Sorry, no linky.
That didn't mention cooling problems, it said it was abandoned because it was LOUD.
Edit: My thinking was to retain the cooling fan and reuse the normally dumped hot air. I don't know if it would increase or decrease the backpressure in the exhaust. A Porsche-style fan would allow tuning because they are available with five to eleven fan blades.
A rear or mid-rear engine or radiator should have the advantage here.