To start with the F3 is a temperature error as you might have guessed and basically what happened was the electronic control sensed a higher than expected temperature and locked the door for safety. As long as the temperature remains high, the door will remain locked and nothing except cycling the power will unlock the door. The temperature must have been pretty high because if both elements no longer work, most likely your thermal overload (AP3885687) located on the back of the oven has opened the circuit and now needs to be replaced. While you are back there, you can check the oven sensor operation by taking a resistance reading at the connector (the one with the violet wires attached) and see if you about 1080 ohms at room temperature. Way high or way low, then it needs to be replaced.

As for the reason this happened, either the temperature sensor was giving high readings to the control board, or a relay on the control board kept one of the element on the entire time instead of cycling as it should. My guess is the sensor is fine since the open thermal overload is a good indication it really was hot inside the oven. So that would leave the oven control. You may be able to replace the overload and have it work just fine. But I would keep an eye on it during the short term and verify you hear the normal clicking coming from the control board while you are cooking. If it runs away again, shut off the power at the breaker and replace the control board (AP3177932).