Given a pot of boiling water at one atmosphere pressure: Turn up the temperature of the burner. More heat (energy) is transferred to the pot down the temperature gradient as the water continues to boil at 100 C. Latent enthalpy of phase transition of one gram of water at 100 C to one gram of steam at 100 C is 540 cal/g. Faster heat input means faster rate of boiling.
Note that a 100 C boiling point only obtains at the surface. The bottom of the pot has hydrostatic head and therefore a higher boiling point. Sufficiently high temp at the bottom will get that boiling, too, resulting in faster heat transfer than mere convection. Too high a temp will obtain the Leidenfrost effect, suddenly dropping heat transfer to near zero. This is a tremendous problem in heat exchangers.
Leidenfrost temperature versus liquid, surface, and surface composition.
The world in non-linear. Do not believe engineers who think a line behaves as it travels to the right. Oil storage tank fires fought with water accumulate heating water at the tank bottom, under the hydrostatic head of the tank. The water superheats util it pushes the oil above it away, then it flashes to steam, expanding a thousand-fold, removing more hydrostatic head...resulting in a BLEVE. The expanding cloud of oil mist and steam, if ignited, is a fuel-air explosion. People get infrared thermal burns hundreds of meters distant.