Abstract The thermal regime of a small celestial body, Kuiper Belt object (20000) Varuna, is considered in the process of its formation by accretion of the protoplanet cloud material as well as during its further evolution up to the present time. We have simulated different formation scenarios of Varuna by varying the accretion time, accretion rate, and a fraction of impact kinetic energy converted into heat. A possibility is studied of water ice existence in the body of the planet taking into account the accumulation of radiogenic heat sources. It has been shown that some scenarios of the planet formation permit to retain the water ice in the planet body up to now.