Final answer:
Using the concept of algor mortis and assuming the maximum cooling rate, Jane Doe's estimated time of death is roughly 14 hours before her body was discovered at 10 AM, which would be around 8 PM the previous evening. This is an approximation as actual determination of time of death can be affected by many factors.
Step-by-step explanation:
To estimate Jane Doe's time of death using the information provided, the concept of algor mortis, which is the change in body temperature following death, can be applied. The average normal body temperature is 98.6°F (37.0°C), and after death, the body typically cools at a rate of approximately 1-1.5°F per hour under typical indoor conditions. Jane Doe's body was discovered with a rectal temperature of 78°F and the surrounding room temperature was 72°F. Ignoring any external factors that might affect the cooling rate, if we assume the maximum cooling rate of 1.5°F per hour and a starting average body temperature of 98.6°F, the difference in temperature from the norm to the temperature at the time of examination is 20.6°F. Dividing this by 1.5°F/hour provides an estimated time since death of approximately 13.7 hours. Thus, Jane Doe might have died approximately 14 hours before her body was discovered at 10 AM, which would be around 8 PM the previous evening. However, it is important to note that this estimate can be affected by numerous factors, and actual determination of time of death can be more complex.