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The temperature distribution in a VVER fuel element with deep burnup of nuclear fuel is studied. Numerical and analytical methods are used. It is shown that a stationary temperature distribution is established in no longer than 1 min. Analytical methods are used to obtain the temperature dependence of the radius of a fuel element in a stationary regime.One way to realize down trending fuel-cycle costs in nuclear power is to increase the burnup of heavy nuclei. Higher burnup is desirable from the standpoint of a positive solution to economic questions as well as to draw high-enrichment uranium and plutonium into large-scale nuclear power, since the transition to deep burnup and long fuel run is impossible without increasing the enrichment of or adding plutonium to uranium fuel [1].With deep burnup of oxide nuclear fuel, a large change occurs in the structural-phase state, chemical composition, and density of the fuel kernel of a fuel element [2]. As fission products accumulate, the oxygen potential changes and new localized phases precipitate [3,4] and the thickness of the most highly damaged surface layer of a fuel pellet increases [5,6]. In the peripheral layer, the initial grains with typical size ~15 μm disperse under irradiation into 0.2-0.3 μm subgrains and low-density dislocations. The result is that a fine-grain structure with elevated porosity of quite large size (micron) forms in the surface layer of the pellets as burnup increases and fission products accumulate. For example, with average uranium burnup 105 GW·days/tons the local burnup in the surface layer of a pellet reaches 300 GW·days/tons. In the process, a so-called ultra-high burnup structure [7-9], where the pore size reaches 15 μm as a result of coalescence or migration of bubbles, forms, increasing the local porosity to 22% [10].The thermophysical processes in the fuel composition and in a fuel element as a whole are of scientific and practical interest. For oxide nuclear fuel, as burnup increases, the thermal conductivity decreases noticeably as a result of the accumulation of soluble fission products and the formation of radiation-induced defects due to the action of fission products. This decrease of the thermal conductivity is especially strongly manifested at temperatures below 1000 K.The strongest changes can occur in the surface zone. It is important to know the particulars of and regularities in the variations of the state and properties of the fuel composition to refine the fuel element design, choose the operating regimes of the reactor, and predict the behavior of fuel intended for deep burnup.For a fuel element as a source of nuclear energy, the thermal conductivity of the materials and heat transfer in the radial direction are important but difficult to determine experimentally. For this reason, it is of interest to perform a theoretical analysis and modeling of the heat transfer taking account of the surface layer, appearance and growth of an oxide layer on the zirconium cladding, and decrease of the gap between the fuel composit...