Someone please explain how ignition timing relates to engine temp ?  

I'm not sure, but I believe when the timing is retarded, the fuel is still burning by the time the exhaust valve starts to open. This would cause the exhaust temperature to be much higher than necessary, and would lead to burning of the exhaust valve.

In contrast, when the timing is too advanced, the fuel burns before the piston hits the top of the compression stroke and you get knocking and pinging, which will eat a hole through your piston. I'm not sure whether this also causes excessive engine temp, but it seems like it would.

I know that if you run your fuel/air ratio too lean, you definitely run hotter, which makes (a little bit) more power, makes more NOx emissions, fails your smog tests, and I also believe it burns holes in your pistons.

Someone else jump in and let me know if you agree with me.  

Actually, you've got it backwards. Advance makes the exhaust hotter because you're firing the spark plug longer in the cylinder. In the 70s when lean burn systems were being employed for emissions, the timing was super advanced to burn as many hydrocarbons in the cylinders as possible to clean up the exhaust.  

Actually either or both too much or too little advance for diffetrent reasons.

Too little results in a late burn, this results in too little of the available pressure and heat being turned into work, so the engine is pushed harder to get the necessary effort, this runs cooling temps up. Along with this is too much heat rejection into the exhaust which super heats the short runner which results in cracking of the casting and excessive heating of the coolant. Late burn while easy on NOx emissions, really runs up the unburnt HCs and puts out a lot of CO since the reactions aren't going to completion. If you have catalytic converters they'll get really hot as they try to complete these reactions.

Over advanced ignition results in excessive pressures and temps before the piston reaches TDC. This of course can lead to detonation and preignition, but it also, leads to overheating from the piston being driven backwards against crank rotation which overheats the combustion chamber and the piston crown. Both the coolant and the oil get very hot. This really increases NOx emissions. Plus the engine is on the edge of serious damage.

One has to be careful when comparing timing solutions used for emissions contol as "rules of thumb"

Low compression and lean mixtures can accept more advance because the mixture being both not compressed much and lean, will burn slowly, therefore more advance can be applied. At low to moderate speeds the manufactures played with retardation to reduce NOx, this is in conjunction with low compression, close to correct mixtures and EGR. So one has to be careful about taking these "emission solutions" and applying them as general rules. There has to be a set of circumstances or ground rules applied to these things.

Bogie