I've got a very similar problem on a very similar range - could be the same model based on your pics. Mine is model RF396LXEZ0.

Every so often, usually when cooking at a high temperature (e.g., tonight it was a 450 degree bake), the oven will magically go into self cleaning mode and can't be taken out of this mode.

Usually this happens when I'm not home but tonight I witnessed it.

I don't know exactly what my wife did but when i got there the display said "cool", but the broiler element was red hot. Any button press caused a beep.

I turned off the breaker, and turned it on again after maybe 30 seconds or a minute. It returned to the same state. I turned the breaker off, and cooked dinner on the grill. :) After dinner I powered it back up, and the control panel indicated "done" and the door solenoid opened back up.

The obvious fix seems like replacing the controller. Anything else I should be worrying about? A bad thermometer sensor that is tripping a cleaning mode fail safe maybe?

thanks