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Early evolution of trans-Neptunian objects, commonly known as Kuiper Belt objects (KBOs), is the result of heating due to radioactive decay, the most important source being 26Al. Several studies are reviewed, dealing with the long-term evolution of KBO models, calculated by means of 1-D numerical codes that solve the heat and mass balance equations on a fixed spherically symmetric grid. It is shown that, depending on parameters, the interior may reach quite high temperatures. The models thus suggest that KBOs are likely to lose the ices of very volatile species during early evolution; ices of less volatile species are retained in the cold subsurface layer. As the initially amorphous ice is shown to crystallize in the interior, some objects may also lose part of the volatiles trapped in amorphous ice. Generally, the outer layers are far less affected than the inner part, resulting in a stratified composition and altered porosity distribution. It is further shown that the thermal evolution of KBOs cannot be treated separately from their accretional evolution, as the processes occur in parallel. A systematic attempt to calculate accretion and thermal evolution simultaneously is presented, based on a numerical moving grid scheme. The accretion rate is obtained from the solution of the coupled coagulation equations for gravitationally interacting planetesimals. The effect of planetesimal velocities on the accretion scheme is included by a simplified equipartition argument. The time dependent accretion rates serve as input for the numerical solution of the heat transport equation for growing bodies mainly heated by radioactive decay of 26Al, allowing for phase transitions. Calculations carried out over the parameter space [heliocentric distance; final radius; ice fraction] lead to conclusions regarding the structure of KBOs, such as melt fraction, or extent of crystalline ice region.