Welcome to the forum
Does the CEL(check engine light) work?
It should come on when key is turned on and then go off after starting engine.
If not then bulb is burned out.
If it takes 45 minutes to warm up then you need to replace the thermostat, for sure.
It has failed OPEN, which is what it is suppose to do when it fails, if it fails closed engine overheats.
Should take any engine no more than 5 to 10 minutes for full warm up depending on outside temp.
When any engine is cold it needs extra fuel, and a higher idle, to run well, thats what Chokes were for on carb engines.
Fuel injection doesn't change that, a cold engine is still a cold engine, and a Choke plate won't work with fuel injection, so the computer that runs the fuel injectors needs to know the engine temp so it can add extra fuel when engine is cold.
The computer uses the ECT(engine coolant temp) Sensor for this temp reading.
The ECT sensor has TWO wires, and it looks similar to the ONE wire temp sender used by the dash board gauge.
ECT Sensor on the 2.3l is on driver side of engine towards the front and below intake manifold.
You can usually see it better by looking thru the drivers side wheel well above frame.
This would NOT delay warm up, it only reads temp, but it could be causing rough running and low power if it is reporting a warmer temp than actual cold engine temp to the computer, computer is not running engine rich enough, but after engine does warm up it would run OK.
ECT sensor is $6-$10, so while you could test it, it is usually just better to replace it.
And since coolant must be drained to do this, I would do thermostat and ECT sensor at the same time.