ADDitionally energy state intertia is hard to break.

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Acceetation requires more energy than the steady system of incremental steps.

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Fast heat-up does requiere additional acceleration effort of the process.

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Slow build-up and then a faster heating up could work and maybe shorten the total time by about 25%-30%

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Like a boost at 60°C to 80% is much easier than working with cold water.