Toyota Corolla 1991 occasional starting problem

Hey,
I've been having this problem with my 1991 toyota corolla. It'll wok fine most of the time but every once in a while it just wont start. And if I wait for half an hour and then try to start it back up and it starts. It usually happens when its left out in the heat.
Well im not really sure what the problem is because it could be because something is running when the car is off and draining the battery or something regarding the engine heating up and needs to cool off. Well the only other useful information I could give you is there is a humming noise when I try n start up the car when it wont start.
Had a mechanic look at it and he changed the starter had all the fluids and oils changed. But it was of no use because the problem still persists.
Hope someone could help me out its really annoying.
Thanks Josh