The engine computer and temp gauge don't share a coolant temp sensor.
Computer uses a TWO wire ECT(engine coolant temp) sensor
Temp gauge uses a ONE wire ECT sender.
Computer bases fuel mix on coolant temp and whether or not to run engine in Choke mode: rich mix, high idle and advanced spark timing, just like choke plate did on carb.
If ECT sensor is not increasing in temp after engine starts, or if ECT fails to reach 185degF after 10 minutes, the Computer will set a code telling driver of this issue, 21, 51, 61 are ECT codes.
Dash board temp gauge is easy to test, locate ECT SENDER, not sensor, it has only ONE wire.
Turn on the key, temp needle should move but just a bit.
Unplug the wire from the Sender, needle on gauge should drop lower.
Now Ground that wire, no it isn't a short, this is how the gauge works.
With that wire Grounded needle on gauge should go all the way to the top.
Some gauges will do the reverse of above, depends on the wiring.
So wire disconnected needle goes to top
Wire grounded needle bottoms out
As long as you get Full peg to peg movement the gauge and it's wire are OK.
If you don't get full swing of the needle then wire or gauge has a problem.
The ECT sensor or ECT sender just report coolant temp, computer has no control over engine temp, that is strictly a mechanical issue.
I guess first question is................is the engine actually running cold?
Is the heater only warm not hot?
If so then I wouldn't think BOTH the sensor and sender have failed at the same time.
The engine is running cold because of a mechanical issue.
Stock 2.3l thermostat is 192-195degF, some put in 180degF because of mistaken belief cooler is better, it isn't, it actually causes more engine wear and lower MPG.
190-210degF is best operating temp for engines made after approx. 1980
Test your Fan Clutch.
Start cold engine, you should hear fan noise when engine first starts and then that noise should lessen as the fan clutch disengages the fan blade from turning at engine speed, so fan is no longer pulling air thru rad, it is just spinning because of water pump motion.
After 30-60 seconds shut off engine
Try to spin fan, it should spin fairly easy, clutch is open and fan blade can spin.
The way the fan clutch works is that on its front side is what looks like a spring.
The spring is warmed up by the radiator, this heat from the radiator causes metal in spring to expand and this starts to close the clutch causing fan blade to grab more air cooling the rad more.
In cold weather fan clutch may never engage the fan blade, because rad never gets warm enough, this is normal in cold climates.
If your fan clutch never releases the fan blade then fan would be over cooling engine compartment, and this is it's "fail safe" mode, if clutch fails it is suppose to fail locked, because OVER cooling is better than OVER HEATING, lol.
So test it.
The cover in front of the rad is a good idea, it keeps the engine bay warmer, these are often added when you notice a coolant temp drop at highway speeds, because air flow thru rad is over cooling engine bay.
If temp drops more at stop lights then I would look more at the fan causing it, it is pulling air when it shouldn't.
2.3l doesn't produce alot of heat it is a fairly efficient engine in that respect, which is why it can run cooler than it should in cold climates.
Blocking rad is one step, insulating heater hoses is another, the flexible foam wrap for water pipes works fine for that and it is easy to add.