Is this still a temperature probe problem?
The only F3 I could find on Frigidaires was related to the probe

Could the new one be faulty?
Always a possibility but the odds are slim on getting a new probe with the same symptoms as the one you replaced

I have checked the wires for continuity and they seem to be fine.
I would recheck the wires and the connectors on the ends
Make sure the pins are clean and well crimped to the wire itself

If everything is OK then it is probably the control board.
It could be a transistor or IC that is starting to go and switching early
It could be a cold solder joint, sometimes years can go by before they actually cause a problem.

Both of the above can be related to the board heating up.

This is a long shot but may be worth a try
Unplug the unit
Remove the connectors from the control board. Clean all plugs and receptacles with isopropyl alcohol or electronics contact cleaner and a toothbrush. Be gentle. Do not reconnect them till all the solvent has evaporated