Engine speed/temperature

A question, if I may?
This thread about a Cavalier that idles too fast got me to noticing...
My winter car, no matter the temperature, whether it's
-40 degrees, or it's been driven an hour, always starts the exactly the same.
Starts at what feels like about 1000 rpm, stays there for perhaps 5 seconds, then slows to about 600. At that point it's idling rough, feel the engine in the steering wheel.
Add to that, mileage is incredibly bad; though I'd put that down to warm up idling, and short trips, few and far between.
Is it worth wondering if the coolant temp sensor should be preventing it from slowing until it's warmed a bit? No codes set; should I change it just to see?
Thanks in advance for any tips.
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