running lean and engine damage

Hey guys heres my latest semi-embarrassing/very honest noob question.

About two weeks ago, someone pointed out that I was perhaps running a bit lean. After correcting the problem, my car is idling much better. I've read running lean means running hot which means engine wear.

so a two-three fold question: (answer anyone you can/care to)
1. why does running lean mean running hot? whats the physics behind this at a layman level. (surprised I couldnt find this on the nets, but I havent always been the best searcher)

2. How quickly can running lean damage my engine? my temp gauge was getting to about the 1/3 of the way to the H and I may have driven her for about 4000 miles like this. :angry7: (can I tell if I did damage? ) I'm gona look closely for any metal in oil when I change it soon, any other signs of damage I can look for?

thanks in advance