Modern gamma spectrometry provides unique opportunities for various studies in many areas of knowledge. Currently, various types of gamma detectors are used, among which semiconductor detectors from high-purity germanium (HPGe) occupy a leading position. The main feature of these detectors is the need to cool the HPGe crystal up to the liquid nitrogen temperature. With the advent of commercially available electromashine coolers (EMC), the development of HPGe gamma spectrometers based on such coolers became possible. The basis of the gamma spectrometer studied in this work is a cryostat with EMC. The basis of the work is determined by the analysis of related dynamic processes in order to develop an integrated approach to the design of cryostats, allowing to reduce the effect of typical shortcomings of electromechanical coolers. The object of the study are dynamic thermal and mechanical models of a cryostat with an HPGe detector and an electric electromechanical cooler. The limited cooling capacity of EMC, due to which there are increased requirements for reducing the heat loss in the cryostat, requires a detailed analysis of the thermal model of the cryostat with EMC and identifying the main ways to reduce the heat loss in the cryostat. Mechanical fluctuations, the source of which is EMC, cause vibrations of the HPGe detector itself and the cryostat cover. Changes in the electrical circuit parameters caused by mechanical vibrations, shocks, and, in particular, sound vibrations lead to interference in the operation of electronic equipment, which degrades the resolution of the HPGe gamma spectrometer. The work considers a mathematical model of the cooling dynamics of a cryostat with an HPGe detector and a comparison of the obtained results with the created model based on the FEM. Verification is performed experimentally. A modal analysis of the basic oscillatory systems of the cryostat was carried out, the results of which were verified experimentally. An integrated approach to the design of cryostats with EMC on the basis of which the samples of produced scientific equipment are modified.