Even warm water on my body can cool me by evaporation. The thin layer of air serves as an insulator. Tile conducts better than cloth. Compare the relative coefficients of thermal expansion of the contained liquid and the glass container of a tube-shaped thermometer. The liquid must have a much higher coefficient of thermal expansion.
Heat is removed when it is absorbed by the evaporation of the working fluid.
The heat is absorbed in the evaporation of the working fluid in the coils. This heat is then moved outside the refrigerator where it is removed from the gas when it is compressed back into a liquid. Working fluid, an evaporator, a condenser, a compressor and tubing to contain the working fluid. Much of the energy is wasted as heat, thus satisfying the Second Law of Thermodynamics. It will cool the region near them as they sublimate.