As many answered to the first part of your question, heat kills bacteria, and the higher of the heat the faster.
As to the second part of your question, boiling would kill much faster than almost boiling. The reason why is convection. Boiling water is essentially being stirred by the boiling, which causes much faster heat transfer. In a hypothetical world in which you could snap your fingers and make water any given temperature instantly, you would find that 100 Celsius actually kills bacteria significantly faster than 99.
In the real world, though, where water takes quite some time to heat up, you’ve probably pasteurized long before you hit the boil.
Heat causes protiens and nucleic acids to unfold (denature) by breaking their hydrogen bonds that hold them in a certain configuration. The protein unravels and can no longer serve its purpose (enzymes no longer work for example).
Heat can kill viruses as well. Some microbes (Botulism in spores) are much more resistant to heat and can survive some exposure to high tempreatures.
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