That is debatable. I have read that the energy it takes to bring hot water to a boil isn’t much less than for cold. I believe Cooks Illustrated/ATK (or maybe Harold McGee) reported on this. Whether the water is heated by the stove, an electric kettle, or your water heater, it takes energy. Microwaving a quart of water, then adding it to unheated tap water, would probably jump-start the heating with the least use of energy. If you have to run your water to get it hot, at least collect the warming water in a pot or jug and use it for something else, like washing up. Wasting water is a matter of ever-increasing importance.
More significantly, you can cook a pound of dry pasta in 2-3 quarts of water, rather than the higher volumes routinely insisted upon by authentic Italian cooks. Boil the water, salt it if desired, add pasta, turn off the heat, stir, cover the pot, and let it steep, adding 3-5 minutes to the cooking time o9 the package. If it’s stranded pasta, lift the lid and stir midway through. You’ll save water AND energy. Or, if you are organized enough to remember in time, soak your dry pasta in tap water for 90 minutes before cooking it, which cuts the cooking time to that of fresh pasta.
Whenever I turn off the stove or oven, I use the free residual heat to heat up a covered pot of water, which I then use for other cooking, or cleaning up. If the air is dry in winter, I leave the lid off, to humidify the house.