Lycoming 0-540 your PA-28-236 runs I think, from memory. Worked on them as a LAME quite a bit, and flown them once or twice as well.
The engine is not working that hard, as it is installed in a basic PA-28 airframe, but provides better cruise & climb performance. This would indicate that extra power that is installed up front from a standard 0-320 would make it a cold running engine, though their exhaust type system is weird that it does not remove the heat quickly from the cylinder.
The engine actually sounds like a tractor on start-up and idle, but smooothes out in cruise. I think that there is a different exhaust set-up that can be purchased and fitted as an after-market item that could increase effeciency and operating limits on your aircraft. I did fit one to a similar piper aircraft, with excellent results, better fuel burn, quieter, and colder running.
I do not remember much about the CHT's or EGT's, as it was a six place digital system, but did not read figures, only yellow, green and red lights.
Maybe you should have gone the SMA Jet-A (diesel concept) engine as per
www.aero-diesel.com as this would have been far more effecient than what you have now!
Cheers, KP