IMO Boiling fuel in the injector lines.
I have an IO-360. With dual P Mags. Runs well when cold but after flight and or a long taxi, engine runs with lots of missing and sounds terrible, to fix, apply power once the fuel starts flowing the missing seems to reduce BUT it won?t go away until full power for takeoff, that fixes it quickly.
FWIW Just after shut down the top of my cowl is nice and cool to touch but give it 5 minutes and you could fry eggs on it. The bottom cowl stays cool, inside, the exhaust is less than 1 inch away from the bottom cowl but you would never know it. I guess this just proves hot air rises and all this heat is boiling up those little fuel lines on top of the engine. I believe the fuel pressure in these lines is around 4psi and there is not much flow at idle so I think this is the reason for the rough running. I have got used to it now and don?t worry about it. I also open my oil door after shut down to let as much hot air out from behind the engine where my P mags are.