Tungsten oxides are promising materials for their use in solar energy, catalysis, microelectronics. Therefore, obtaining tungsten oxides with desired properties is an urgent task. The aim of the work is to study the patterns of growth of tungsten oxide crystals on the surface of tungsten samples at different temperatures, as well as to study their structure, properties and growth kinetics. The high-temperature stationary regimes of formation and growth of crystalline oxide structures on the surface of a tungsten conductor heated by an electric current in air are investigated. The temperatures at which threadlike crystals appear on the surface of tungsten are determined, the regularities of their growth are investigated. A physical and mathematical modelling of the temperature regimes of heating and oxidation of a tungsten conductor in air is carried out. The results of the calculation of temperature regimes according to the developed model well describe the experimental data obtained by us using the electrothermographic method. Experimental studies conducted are established a physicochemical mechanism of the formation and growth of crystalline oxide structures on the surface of a tungsten conductor. At temperatures of heating up to 900 K, oxidation proceeds without features. A continuous oxide layer is formed on the surface of the conductor and cut by ditches and grooves, which is a consequence of different mechanical stresses in the local areas of the sample. The appearance of the threadlike crystals on the surface of the oxidized tungsten conductor occurs at its average temperatures above 900 K. It is proved that the carbon particles, that are part of the impurity, are the cause of stoning on the primary oxide film of threadlike crystals of tungsten trioxide. With an increase in temperature, due to oxidation, threadlike crystals grow, then branch out and turn into dendritic structures of complex bushy shape. Branched oxide structures are connected with the main oxide by a thin partition. The higher sample temperature leads to the greater rate of sublimation of tungsten trioxide from the surface and the more intense of growth and branching of the oxide crystal structures. It is proved that the rapid growth of crystalline structures occurs as a result of the deposition of clusters and microgranules of WO$_3$ oxide from the gas phase onto crystallization centres on the surface of the conductor, which are carbon particles. Clusters occur due to large temperature gradients near the surface of the conductor. As established, the carbon atoms can migrate along branches of oxide crystal structures. The optical-digital method developed by us allows to observing the surface of the heated conductor in real time and establishing the general laws of growth and branching of crystals. As proved, the crystals first grow more intensively in the longitudinal direction (perpendicular to the axis of the wire), then, upon reaching a certain size, in the transverse direction. The growth rates of crystal structures in the longitudinal and transverse directions are determined. As established, the maximum crystal growth rates are 0.4–0.6 $\mu$m/s. The fractal dimension of oxide structures arising at different oxidation temperatures is determined. This made it possible to clarify the growth mechanism of oxide crystal structures at various stages.