I wonder how many planes will have the engine below say 400F when doing a Vy climb, even with mixture fully rich.
In my limited experience of the higher performance types, probably none of those.
Yet, during training (PA38, C152, PA28-140 -161 -180) we were doing Vy climbs all the way to altitude. None of those planes had any EGT or CHT gauges, however. In the FAA IR (Arizona, ISA+10 or so) we were doing Vy climbs to 11,000ft and the only gauge was the oil temp.
And when people do have a CHT gauge it tends to be on #5 or #6 (on a 6-cyl) which common sense tells you should be the hottest but common sense is usually wrong in this case because it is the middle ones (#3 or #4 - usually #3 if the oil cooler is mounted on that side, robbing some air for itself) which run the hottest. These are typical full-rich deg-F climb CHT figures for mine, #1 to #6
380 359 398 374 386 373 194
where the last one is the oil temp. And that was climbing out of St Gallen LSZR where the OAT was +14C so not exactly warm. Looking at the EGTs, that part of the climb was full-rich, too, trimmed for 120kt to get plenty of cooling air.
You can see #3 is 25F hotter than #6.
So it would not suprise me if a lot of un-instrumented engines out there are being run very hot, because Vy climbs are common on the training scene.