The wider temperature gradient you keep between the ambient air and the water, the higher rate of loss of temperature. If somehow you had a magic levitating engine that converted a heat energy to potential energy, you could use this lost energy to lift the cup of coffee from sea level to 8,500 meters just under the height of Mount Everest. That's an insane amount of energy when you think about it. But at least according to the calculation I did, the difference between mechanical energy and heat energy is just it defies your intuition.