Does a lean mixture result in a higher cylinder temperature for a given power setting? From what I know over rich mixture help cools the engine due to evaporation process and lean mixture do the opposite. 
So why this graph showing when reaching around peak EGT the opposite happens:
To oversimplify, you could say it's because when you are rich of peak you are getting temperature reduction from too much fuel.  When lean of peak you are getting temperature reduction from too much air.  Watch this guy's youtube video seminars.  They are a treasure.