Employees of UrFU and the employees of the Pervouralsk Novotrubny Plant developed and implemented a technological scheme for the production of capillary tubes used for the manufacture of disposable medical syringes. To obtain a given size, the pipes are drawn, after which they are annealed in a continuous electric furnace with a protective atmosphere to relieve stress. In order to optimize the pipe annealing process, based on thermal engineering calculations and developed methods, heat losses were determined, which made it possible to find the installed furnace power. A calculation of the heating elements was also performed, during which the diameter of the wire heaters and their total length were determined. The rationale for the methodology used for calculating the heating time of thin bodies for capillary pipes of a given size is given. Based on the constancy of the temperature of the furnace working space and the transfer of heat predominantly by radiation, the heating time of capillary pipes of different diameters was found. In order to determine the operating parameters of the process of purging pipes with various gases, the calculation of pressure losses for pipes of different diameters and lengths was carried out. Studies are presented to determine the temperature fields inside the muffles. The results obtained in this work make it possible to develop new technological schemes to obtain capillary tubes for the manufacture of medical needles.