I guess start from scratch.
Vehicle cooling systems are pretty simple to understand.
Water pump circulates coolant, it doesn't "pump it" so it adds no pressure, it just circulates fluid, it can't circulate air, air is too thin, it needs to be all fluid in the system.
Smaller hoses, like for the heater core, can get air trapped inside, this will block coolant from flowing into or out of the heater core, so no heat inside the cab but temp gauge shows "Normal" heat in the engine.
Air in the head will show up as overheating on the temp gauge.
Bad water pump will cause overheating, not over cooling.
Radiators purpose is to remove "extra heat" from the coolant, so in cooler weather the radiator may not even be used.
Thermostat sets the lowest coolant temp for radiator circulation, if you use a 195deg t-stat then there will be no flow in the radiator until coolant circulating in the engine and passed the back of the t-stat is at 195deg, at that temp t-stat opens and coolant flows thru the radiator, often the t-stat will close again as the cooler fluid from the radiator comes into the system, then re-open as it is heated up, so if you watch the temp gauge you can often see the t-stat opening, needle goes down a bit as radiator coolant comes in, and then needle slowly goes back up to normal, this can happen several times, depending on outside temp.
Simplest way to test t-stat is to start up a cold engine and feel the block as it warms up, and feel the radiator hose connected to the t-stat housing.
If radiator hose starts to heat up same as the block then t-stat is NOT blocking flow thru the radiator, as it should.
The whole point of the t-stat is to block coolant flow thru the radiator.
So if rad hose is heating up then t-stat is either open or is being bypassed, because coolant is flowing, warmer rad hose is proof of that.
So you either have a bad t-stat or bad seal or some other form of by-pass allowing circulation to the radiator.
Engines are designed to operate with coolant temp between 200-230degs, this gives the best lubrication(oil viscosity is rated at 212deg), and the best economy/MPG.
Running an engine "cooler" is not as bad as overheating, but it is not "good" you will have less effective lubrication, and of course lower MPG.
So lets say the radiator hose is not heating up so t-stat is working as it should, but engine is still not getting warm enough.
Running rich, this lowers the engine temp, rich fuel/air mix cools the cylinders more than normal/lean fuel/air mix.
MAF or MAP/Air Temp sensors malfunction(both can be tested with a simple meter)
O2 sensor, these are not used until engine temp gets to about 180deg, but could still cause a rich fuel/air mix.
Lower overall MPG would be a sign of overly rich fuel/air mix.
EGR system opening too much, EGR exhaust gas cools the cylinders, which reduces N0X, too much will cause cylinders to cool down, poor running is often the result.
Timing is retarded, the more advanced the timing the better/hotter combustion you will get.
Often timing control is not adjustable, but a sensor could be malfunctioning causing timing to be retarded.
Knock sensor, retards timing when engine pings/knocks, the "noise" of the ping may not even be heard by you, the knock sensors uses a frequency detector, if it is defective it could be retarding the timing all the time.
If Base Timing is adjustable then make sure it is where it should be.
A timing light can be used to check timing at idle and then at 2,500rpm, to make sure it is advancing as it should.
And as always never base engine temp only on what the dash board gauge shows, it has three parts, sender, wire, gauge, any of which could be compromised and reporting a lower than normal temp.
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