what temperature thermostat for 2003 3.0 flex

when its cold outside oil pressure gauge bounces

 

Welcome to the forum

192 or 195 degF is correct thermostat for 3.0l
Thermostats have a small hole in the plate, jiggle valve, it should be positioned at 12:00, it lets air out when refilling or ???

Check connector on the oil pressure sender, it is behind the head on passenger side, on the block near bell housing.
It is a SWITCH, so it is either ON(grounded) or OFF(not grounded)

The gauge shows same "Pressure" if SWITCH closed(on) so oil pressure could be 7 to 70, needle wouldn't move, as long as it is above 5psi switch is closed(grounded)
Any slight needle movement, like at higher RPMs is from the alternator, voltage goes up a bit and so does needle

If needle is bouncing then either the wire is loose, or sender/switch is bad
Could be oil pressure is dropping below 5psi but you would also be hearing lifters "tapping", which you do not mention, so.........oil pressure is OK
Wiring issue most likely