Opening the exit area by removing 4" of cowling forward of the exhaust pipes increases air flow through the engine compartment, it helps to cool the engine.
Of course it does. If you install pressure, temperature, and pitot probes you'll find that the upper-to-lower pressure delta is increased, the heat transfer per mass unit is decreased, and exit velocity is slowed. Mass flow is increased faster than heat transfer is decreased, so cooling capacity improves. However, more mass flow plus more velocity loss means more cooling drag.
From McCormick,
Aerodynamics, Aeronautics, and Flight Mechanics:
In plain English, the first equation says:
Cooling Drag = mass x (freestream velocity minus exit velocity)
I often extend an experiment to the ridiculous just to see what happens. Recall my cowl is modified; among other things, the standard cowl's huge exit chute was removed. It is replaced with any cowl panel desired. The panel is attached with #8 screws.
Early in the test program I made a flight with no cowl exit panel in place, the result being a rather large exit. Note, it's not as large as you might think at first glance; actual exit area here is the entrance to the internal converging exit duct.
DA at 3540, OAT at 52F, 170ktas. Pressure delta was 17" H2O, which is a lot, due to near zero exit restriction and no leakage to bypass the fin passages (pressure probes were actually across the oil cooler, but that should be close to upper-lower plenum pressure delta). The interesting values were CHT, and air temperature measured just under the #1 cylinder, where it exits the baffle wrap. CHT's were 267 270 274 286 (very low, as expected), but due to the high volume driven by the large pressure delta, the cooling air was only being heated to 135F during its trip through the fins. Contrast those numbers with typical for this system; CHT around 350F in best power cruise, cylinder exit air temp around 230F, with exit area reduced to about 30 sq inches. That's cooling an IO-390.
Approximately 16 sq in is added for hot day climb, using a variable exit air door. The total is still a lot less than a stock exit.
Visual comparison. This is stock:
30 sq in exit, basically just the depth of the RV-8's belly inset (please excuse all the tape and brackets for test gear)
Open for climb:
Point is, improving heat transfer efficiency allows a
reduction/I] of exit area. In the above example, it is done with extreme baffle and plenum sealing, and a larger than typical oil cooler. Empirical evidence suggests that a parallel valve motor shifts the critical emphasis to CHT, vs the angle valve's emphasis on oil cooling. With either, additional pilot controlled exit area is easily built or bought. Just leave it closed in the winter.