Why the temperature increases from top to bottom on the leeward side of the mountain?

The leeward side of the mountain is the side of the mountain that is covered by wind and you may notice that that side is drier than the windward side, which is the side that faces the incoming wind. 

Now the leeward side temperature increases from top to bottom because when the air goes up the mountain from the windward side, it loses most of its moisture. So by the time the air goes down the leeward side, it lacks moisture and heats up as it loses even more moisture going down. This is called the rain shadow effect.