At the Pervouralsk New Pipe Plant, in collaboration with the staff of the Ural Federal University, a technological scheme for the production of capillary tubes used for manufacturing disposable medical syringes was developed and implemented. To achieve the desired tube size, the tubes undergo drawing, followed by annealing in a continuous electric furnace with a protective atmosphere to relieve stress. To optimize the annealing process of the tubes, thermal losses were determined based on heat engineering calculations, which allowed for the optimization of furnace power. A calculation of heating elements was performed, determining the diameter and total length of the wire heaters. A method for calculating the heating time of thin bodies for capillary tubes of a given size was substantiated. Based on the constancy of the temperature in the furnace’s working space and heat transfer primarily by radiation, the heating time for capillary tubes of different diameters was determined. When blowing tubes with various gases, pressure losses were calculated for tubes of different diameters and lengths. Temperature fields inside the muffles, through which the capillary tubes move, were investigated. The obtained results are of interest to technologists and can be useful in developing technological schemes for the production of capillary tubes for manufacturing medical needles. © Allerton Press, Inc. 2023.