The ideal place to record body temperature in dead body is:

The rectum is the ideal place to record temperature except in cases of sodomy. For about half to one hour after death, the rectal temperature falls little or not at all. Then the cooling rate is relatively uniform in its slope. The temperature can also be recorded by making a small opening into the peritoneal cavity and inseing the the thermometer in contact with the inferior surface of the liver. The external auditory meatus or the nasal passages also can be used to record temperature. Ref: Textbook of Forensic Medicine and Toxicology by K S Narayan Reddy, 27th edition, Page 135-136.