On my 2320, i added an engine oil and water coolant temperature gauge since the factory dash did not have a gauge, only an overheat idiot light.
I store my unit in the garage and always start it at idle and allow it idle until the gauge indicates 100 degrees water temp. Only takes 3-5 minutes when ambient is 65 or higher. Takes about 10 minutes when freezing. After 100 degrees is reached, I idle up to about 2000 rpm and work hydraulics and drive the unit to work area. It usually warms up to 150 degrees for normal op temp as indicated on gauge. Highest I have seen so far was 170 while mowing at 2800 rpm for 2 hours at 85 degrees ambient. Will learn more this summer.
Interesting thing I observed is when I shut her down, I set it down to idle and the temp immediately rises 5-10 degrees as the water pump slows. After letting it idle for 2 minutes, you can watch the temp start dropping as the coolant sitting in the radiator starts to flow and carry the heat away. I wait until the temp hits about 130 at idle before shutoff. Usually takes about 2-3 minutes of idle. Would be curious to see how a Direct injected or turbocharged unit warms up and cools down.