I start my car my cuts off on it own after 20 to 30 min of idle.

What is your question?

will run smoothly and once warmed up if idling it will cut off and not restart but will turn over really strong or I can be driving and it will just shut off on its own unless I am double peddling it but once I shut it off it wont restart for like 30 min or engine has cooled down . What I have done so far is replaced alternator (needed it) , replaced radiator(needed it), replaced spark plugs. still having same problem please help someone I am lost on this.