my car runs great for the first 20 min to a half hour then starts accting up. it will spit and sputter, but if i let off for a sec then hit the gas a little harder it will clear out now its not shiff

So affte its run for a half hour and starts spitting and sputtering, if i stop at a store put it in
park and leave running it will shift hard when i take off. So then if i pull over put in park
and rev the engine a little or shut off for ten min it wil all be fine for a little wile again.
Seems like its loadiing up but why is it shiffing ruff. It only shiffts hard when the engine
acts up. Any input on where to start.