Definitely check for codes.
Since it happens when it's warm and you can shut it off (cool down?) and turn it back on to have it go away for a bit, I'm wondering about the TFI.
My TFI did something a little like this before it actually completely died on me when the truck got warm..Which is typical of a failed TFI Module.
Even though I feel that it's ignition related, Another thought could be some kind of sensor or even the oxy sensor. When a vehicle warms up it, it goes into Closed loop. This means that the computer is "paying attention" to the sensors..especially the oxy sensor that trims fuel levels. When a car is started, the computer is in open loop until certain criteria is met. Especially if cold....The o2 sensor needs to be heated to work properly.
After the sensor is heated up, the car goes into closed loop and the O2 sensor make their corrections.
If I'm not mistaken, I think this also effects other sensors like the TPS, MAF, ect.
1st things 1st though...I'd check for those codes before messing with it and potentially wasting money.