The question involves energy and the transformation of a liquid (water) to a gas
(vapor).
Simple case: Use 100 degrees (arbitrary units) of energy between freezing (0) and boiling (100), or 180 degrees between at freezing (32) and boiling (212).
Real world: When the average amount of random energy in water breaks molecular bonds, and the molecules are free to form a gas, the water boils.
Answer: Water can boil without being hot.
Examples:
Water boils at lower temperatures in high elevations.
Cold water will boil when placed in a vacuum.
Kelvin extrapolated the Celsius scale to an unreachable absolute value
of -273.15 ºC.
Mathematics
Water thermodynamics are equated using statistical mechanics.