If you have exhaust vents on the top of your cowl this will minimize that condition. But there has been discussion about increased drag from them in flight. For me they help inflight cooling by aiding airflow out of the exhaust end of the cowl...
Like Harry, I added a set of exhaust vents on top of the cowl above the cylinders in the form of louvers that direct the air aft, pretty much tangent to the flow over the cowl. The main incentive was to improve ground cooling after I went to a longer extension that reduced my ground cooling a bit by moving the prop away from the cowl exit. Overall, I'd say that the louvers help cooling on the ground somewhat, and reduce the internal shutdown cowl temps (you can feel plenty of heat coming out the 'chimney' after shutdown since, indeed, heat does rise!). Still, the cowl gets plenty hot, but it's not a problem. I didn't notice any significant drag increase adding the vents (I'm sure that there is some); however, it is definitely important to avoid any 'rooster tail' airflow out of the plane (like straight stacks that point down, air leaks out of the canopy, etc.).
I have seen, on a tractor type plane (glassair) one that the owner had installed some hinged doors that hung down open when the plane was not moving but when pressurized in flight were pushed closed but I don't know if that would work in our situation...
I haven't seen this personally, but I understand that there are at least some EZs that have done this 'drop down door' approach using the oil access door. It's supposed to definitely help reduce the in-cowl temps after shutdown (which, short of burning up the cowl paint, is really what you care about).
Is this normal after engine shutdown?...
Obviously, it always helps to park facing into the wind since hot air doesn't like to flow backwards, down and then out of the cowl (assuming you have updraft cooling, of course). But the bottom line is - yes this is normal for EZs and not a problem if your paint is OK.
