Question

Why a thermometer is kept only below our tongue, underarm or ear

Answer 1

You are trying to find the core temperature of the body. The only way to truly do that is to stick a thermometer in your core. Since that is rather painful, we instead look for areas of the body where there is a lot of blood flow since the blood carries heat from our core out to our extremities.
The tongue has a lot of blood flow. The arm pit is well insulated and has arteries near the surface and it tends to collect heat. The ear penetrates a decent distance into the skull and tends to give a good measure of radiant heat, also blood vessels.
And , other openings to the body also have a lot of blood flow and get you closer to the inside temperature.