What causes engine to idle rough and hesitate when driving after reach normai operating temp?

Could be many things. My first guess would be a vaccume leak.

When a fuel injected car reaches normal operating temperature it goes from what's called "open loop" to "closed loop"

Under "open loop" the car runs on default factory settings. After it reaches operating temperature, if nothing is wrong (as far as it knows), it goes to closed loop operation. While in closed loop operation it uses the data from all the sensors to fine tune engine operation. If you have a faulty sensor reading then the computer will adjust fuel and ignition incorrectly.

Carburetors have a similar function. It's called "choke" It is a butterfly valve that restricts air flow causing the engine to suck in more gas and less air from the carburetor. The result is a richer mixture. When the car warms up, the choke turns off (if working correctly) and if there is a vacuum leak, it will suck in more air and cause the car to run lean and misfire.

If it starts hard too I would suggest a tune-up.