The numerical simulation of heat transfer was conducted in a cascade of thermosyphons representing a system for extracting geothermal energy from great depths. We proposed a mathematical model of heat transfer in the coolant layer on the bottom cover of a thermosyphon and in the vapor channel differing from the well-known ones by a simplified description of the complex of thermophysical processes occurring in the evaporation, transport and condensation zones of the thermosyphon. The aim of this work is to develop a simplified method for calculating temperature fields in a cascade of thermosyphons, which makes it possible to conduct design and experimental work to create the systems for extracting geothermal energy based on a cascade of thermosyphons. The boundary problem of mathematical physics was solved by the method of finite differences. We showed the possibility to analyze the main characteristics – temperatures – within the framework of the model of «effective» thermal conductivity. The transfer coefficients of this model can be determined experimentally. We found the possibility of heat transfer from large depths with «efficiency» sufficient to achieve temperatures of about 330 K in the heat supply system when the external contour (thermosyphon surfaces) is completely thermally insulated. The results obtained are the basis for the further development of models and methods for analyzing geothermal energy extraction from great depths using a cascade of sequentially operating thermosyphons. According to the obtained theoretical results, the main directions of experimental studies were formulated to justify the conclusions made by the results of a numerical analysis. The results of numerical simulation provide grounds for concluding that the future (experimental and theoretical) development of a method for extracting geothermal energy from large depths of groundwater using a cascade of thermosyphons is promising.