As heat is added to water, is it possible for the temperature measured by a thermometer in the water to remain constant?

Yes, IF The water is at the boiling point. Then the added heat goes to change some of the water from the liquid phase to the gas phase, without changing the temperature.

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Aform of energy that is reflected or emitted from objects in the form of electrical and magnetic waves that can travel through space. there are many forms of  electromagnetic  energy including gamma rays, x rays, ultraviolet radiation, visible light, infrared radiation, microwaves and radio waves.