An Isothermal Core is a central region of a body (planet or star) that is all of the same Temperature. In "everyday life", the higher pressure results in a higher temperature, so the temperature generally varies by distance from the center of a body held together by self-Gravity. Under some conditions such as very high temperatures and pressures, the Ideal Gas Law may not apply, and this temperature/pressure relationship does not exist. If there is also no energy source present (such as Fusion), a spherical region centered on the body's center may all be at a single temperature.
Isothermal cores have been proposed as likely in some types of planets and stars, including Neutron Stars and some Giant Stars. Simulations and other models are sometimes created using an isothermal core as a likely-reasonable approximation.