4 degrees Celsius - 60 degrees Celsius is the 'danger zone' aka when food spoils.
In Fahrenheit, the Temperature Danger Zone is considered 40°F to 140°F. The concern here is actually about growth of pathogens. Spoilage occurs at temperatures cooler than 40°F, as anyone who has cleaned out a refrigerator can attest. Spoilage always has a time-temperature relationship. The warmer it is, the faster it will spoil. Thermophiles can cause spoilage above 140°F, but pathogens don't like that temperature.
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Yogurt is made by culturing milk with bacteria at temperatures that are ideal for the bacterial strains being used. That is usually above body temperature. You could say it is already spoiled. Older yogurt will have a more bitter flavor due to continued bacterial growth.
Temperature most certainly does affect how food spoils. Freezing will stop the growth of spoilage organisms, but it can still become rancid - which could be considered a type of spoilage. Refrigeration slows the growth of most spoilage organisms - but doesn't stop it. Most spoilage and pathogenic microbes like the same temperatures we do and will grow rapidly at temperatures we find comfortable.