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Temperature would speed up the fermentation process until a certain point. At approximately 55 degrees Celsius, the yogurt cultures would be destroyed.  

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The function of the starter cultures is to ferment lactose (milk sugar) to produce lactic acid. The increase in lactic acid decreases pH and causes the milk to clot, or form the soft gel that is characteristic of yogurt. The fermentation of lactose also produces the flavor compounds that are characteristic of yogurt.