It’s a large strongly circulated internal organ, that’s fairly easy to stab a thermometer into. Because it’s internal and strongly circulated, as long as your heart is still beating, your liver temperature will be at body temperature. There’s no real way for external influences to depress your liver temperature whilst you’re still alive, and because it’s internal with no direct exposure to the environment and so large, it cools fairly slowly and steadily, so you have a relatively long window after death where the liver is still warm.
The body’s temperature drops after you die and a rate that depends on the surrounding temperature.
The liver is a large internal organ relatively easy to access and is an easy place to measure a very accurate temperature. A rectal measurement is easier and is often done instead even if ti is a bit less accurate.
The temperature inside your body is pretty consistent. Everyone have the same core body temperature to a few degrees. So we know the temperature of the body at the moment of death. The body then cools down over time until it reaches ambient temperatures. How long this takes depend on the temperature and environment so these are important factors to consider as well. The outside of the body, near the skin, cools down first and the further away from the skin you get the longer it takes for the body to cool. The liver is pretty much in the centre of the body. So it is the last organ to cool down. Police are able to take the temperature of the liver even if the rest of the body have cooled down. They can then look up in tables depending on the surrounding environment and the weather data of the area. This gives them a rough estimate of how long the body have been dead for.
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