Time to boil is just heating power and time. There are two parts of this: the starting temperature of the tap water and the starting temperature of the equipment (stove, burner, kettle).
If your tap water is 40 degrees F/5C, then it needs to be heated by about 170 degrees the first time. But also everything else is starting at room temperature (70F/21C). So all of that needed to be heated first before the water temperature would increase.
But if your teapot *starts* warm, and the stove burner *starts* warm, more of that energy goes directly into the water, which can’t cool below room temp. So your tea was at least 35+ degrees F closer to boiling, and the equipment you used to boil it was also preheated, so it re-boils in less time.
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