GE Profile Oven temperature varies wildly

SOURCE: Oven does not start

This is an update from James758. When I pressed the temp sensor probe and wiggled it a bit, sometimes the oven would work, but then it failed permanently after a few days. Had to call a repairman who charged $325 to replace the entire electronic panel and the separate sensor, although the failed part was only a relay on the board according to him. He also found a pinched wire when he pulled the oven out (one new electronic board relay failed when he first replaced it). Don't know how the wire to the sensor got pinched since the oven worked for 8 years without us moving that hidden wire. By the way, buying the sensor at a parts store in town was $18 versus his cost to us of $49. I'm sure the electronic board would also be much cheaper online. My wife watched the repairman replace the parts; you can save a lot of money doing it yourself.

SOURCE: GE JTP 1580W288 Set oven to Bake, switches to broil at bake temp

The F2 Error code means the oven has detected an excess temperature condition. Most often this is due to a bad temperature sensor - the sensor costs about $75 from an online repair site. 
How to remove and replace the temperature sensor. In most GE ovens, when you open the door, you'll see the rod-shaped temperature sensor sticking out of the back wall at the upper left. It's about six inches long and a bit more than 1/8" in diameter, held in place with two screws. 

Turn off the circuit breaker (built-in ovens) or unplug the range before attempting the replacement. 

The replacement sensor will come with instructions, but basically it's a matter of removing the sensor, pulling out the wires to where they are connected and disconnecting them. You may have to snip. The replacement sensor will come with high-temp wire nuts to hold the new connection. Polarity doesn't matter; it's a straight resistance thermocouple. Hook it up, be sure you poke the connections back far enough so that they're on the other side of the thermal insulation and not resting against the back of the oven. 

If you continue getting the F2 error after replacing the sensor, then the problem is likely in the control module - this is the circuit board behind the keypad and clock. 

You'll need to remove the decorative bezel to get behind the control panel. Remove screws and set off parts in order - it's not complicated. Once the bezel is off there are two more screws that hold the panel in place. Then you can lift the panel up about a half inch and pivot it forward toward you. You'll see a bunch of wires going to a circuit board. 

On the panel you will notice some black plastic boxes that say "Potter & Brumfield" on them. These are relays. Check the relays - slide the black plastic cover straight up to expose the coil and the contacts. The coil, when energized, closes the contacts - look at all the relays. You can manually close the contacts with your finger (be gentle). If the contacts of one of them are stuck, they might be welded together. You can fix the problem by prying apart the welded contacts gently with a knife blade. Take some time to gently polish the relay contacts with a folded bit of fine grain sandpaper - this will get some more life out of them. Be gentle and careful - the relays aren't complicated but if you bend the contact or rip it out, you'll have to replace the controller, which will set you back a couple hundred dollars. If you unstick and burnish the relays, they will probably eventually weld together again as the rough spot will spark, but when you burnish them with sandpaper they should be good for some more life before they need to be replaced. 

If the problem isn't the temp sensor or welded relay contacts then the problem is obviously somewhere else, but temp sensor and relay contacts will account for the lion's share of F2 errors. 

Once again, be safe, be careful, be gentle. Ovens are not very complicated and they're tough, but always exercise care. Always disconnect electricity before messing with them.
good luck,