Simply put, you look at CHTs to look for problems. Rapidly rising CHTs are a sign of concern, as are excessively high CHTs. High CHTs are indicative of high internal cylinder pressures, which put stress on the engine. And hot metal is weak metal. You add these two together, and you have a recipe for damage.
Rapidly rising CHTs can result from detonation and preignition. Those are bad and require immediate action. Look for a CHT trend on the take-off roll; if something is wrong here (e.g. misfueling), responding to an unusually rapid rise of CHTs will be your only possibility of detecting a problem before you are in the air.
EGTs are simply a means to assess how you have set your mixture; specifically, where is your mixture in relation to peak EGT. There is no good or bad EGT; instead, you choose a mixture setting that results in a desirable compromise between performance, engine temperatures (CHTs) and mechanical stress, suitable for the phase of flight you are in. Contrary to popular belief, there is absolutely no advantage to having the EGT bars all neatly aligned on the engine monitor.
Oil temperature is also important. Make sure it's warm enough before you do the run-up and take-off. Taxi? Unless you are parked in the grass, it takes so little power to taxi that I am not concerned about it. In cruise, you want the oil warm enough to get rid of water (which is why in the winter months I tape off part of the oil cooler).
Shock cooling? People who understand engines much better than I do call it a myth.
If you are in Oshkosh, you can come to my engine management seminar on Monday (10AM, EAA Forum Stage 4) or Tuesday (11AM, American Bonanza Society tent) and we'll go over all of the above in much more detail.
- Martin