Step 1: Estimating time since death from body cooling needs a reading that mirrors the internal core, not a surface zone affected by the environment.
Step 2: The rectum satisfies this requirement best; the thermometer goes in roughly 8 to 10 cm and is left for about 2 minutes for an accurate deep reading.
Step 3: Alternative deep sites occasionally used are the nostril, ear canal, vagina, and the area beneath the liver.
Step 4: Mouth, axilla, and groin are too superficial and prone to environmental error, so they are discarded.
\[\boxed{\text{Rectum}}\]