I have a 2004 Suburban Z71 with 205K miles.

QUESTION: Should the radiator fan run at initial start-up when the engine is cold?

I have never noticed whether it runs or not when you start the engine from a cold start. Yesterday, I noticed that the dashboard temperature gauge wasn't operating; e.g. the needle was sitting at/just below 160 degrees after driving for 30 min or so. I thought the engine coolant temp sensor was bad, but this morning the dash temp gauge was reading properly. I also noticed that the fan was running from a cold start. Since the fan is connected to the water pump pulley and the water pump is continuously running when the engine is operating, shouldn't I expect the fan to run continuously as well?

As an aside, the cooling system has always been properly maintained and the water pump was replaced at 150K miles.

Matt