I went thru a similar situation after install a new Lycon engine in a pa 18, difference being, I was flying behind a proven cowl design that was more than adequate at cooling previous engine.
Maiden flight #3 cyl was flashing 450° (JPI) and climbing as I passed thru pattern altitude. I immediately returned to the field thinking I had left a rag or something on top of the engine. Thorough inspection revealed nothing obviously amiss so I went back up, same thing, all cylinders temps were Climbing thru 450°, it was impossible to push the engine hard enough to insure good break in.
landed, thoroughly went over the engine, checked mag timing, fuel flow at carb, etc.. nothing amiss.
I had sent the engine to Lycon for their hot rod treatment and was now embarking on a long arduous journey to figure out how to make it flyable.
Fortunately, this occurred during “winter” (so cal),
waking up at predawn i was able to take advantage of 30° mornings and fly enough to successfully break cylinders in.
Recreational flying was pretty much out of the question.
Thru a tip I picked up on the vans chat board, started to focus on carb mixture and “leaning authority” - how many deg rop the engine was running at various power settings with mixture knob full rich.
pen and notebook in hand, I embarked on a test flight recording temp spread between full rich and peak while leaning, beginning at 2100 rpm thru 2700 rpm on hottest cyl.(#3)
At 2500rpm, full rich, I was 20 rop.
that will destroy a motor in pretty short order. (Ideally looking for 150° rop at 2500)
long story short, solution was to drill main “jet” in carb incrementally until I was able to run 100° rop full rich at 2500
this made the plane flyable, and combined with several cooling mods similar to what Ted has described, I’m now happily climbing out on 80° days at 380° hottest cyl.
Horsepower creates heat, cub type aircraft fly too slow to get rid of heat, adding a long prop makes it worse.
For what it’s worth, this was the solution to my high cht issues, SQ2 is a different animal..
disclaimer: “drilling” the fuel nozzle requires proper tooling - lathe, drill followed by reamer followed by de burring, I’m not encouraging anyone to take this operation lightly.