Why measure body temperature in the ear?

Ideally, you'd like to know core body temperature, which is the temperature of the vital organs, such as the brain, the heart etc. In-ear measurement has the benefit of providing information about brain temperature because the eardrum (i.e. the part of the ear that we measure) shares the same blood supply as the part of the brain that controls your body temperature. The in-ear measurement also responds quickly if there is a change in temperature.

Source: K. Parsons. Human Thermal Environments. The effects of hot, moderate, and cold environments on human health, comfort and performance. 2nd edition, 2003, Taylor & Francis, London.