Starter only starts when engine is cold

My car is having an odd problem. When the car is cold or has only been driven a few miles or few minutes it starts up without hesitation. New battery just installed. Now two times after driving the car like thirty to forty minutes once it is turned off it will not start until the engine has completely cooled down. Several hours later. Then boom starts. The engine does not register hot, but it does have a different smell sometimes. Just had the oil changed too. All fluid levels are fine. What could cause this?