I’m not sure about your point about “more coarse”. Do you mean setting a lower RPM for a CSU-equipped propellor? Lower RPM doesn’t necessarily reduce CHTs.
Two identical engines at full power. One more coarse than the other. The CHT should be lower on the somewhat more coarse one. Within reason though, I'm not talking full fine versus full coarse. Difference in airflow, speed, rpm, fuel burn and load. It was just a minor observation.
The problem with flying in this weather is that you're so close to the manufacturers maximum OAT, plain and simple, so it's always going to show high temps, you can't help that. The best you can do is try and keep them low, knowing that high temps will of course in time do damage, but balance that with the other 10 months of the year. Hence the reason when touring why many choose to fly in the early mornings where possible, particularly up north.