Energy demand and growing environmental concerns have fueled increased interest in geothermal drilling in recent decades. The high temperature and pressure in the boreholes present significant challenges to drilling, particularly in terms of the selection of suitable drilling mud, cement slurry, and drilling equipment. Drilling mud is regarded as one of the primary factors that affect the cost and success of geothermal drilling. This paper presents experimental studies aimed at assessing the thermal stability of drilling muds for geothermal drilling. Research on the antidegradation of polymers contained in drilling muds is presented. The thermal stability of drilling fluids was evaluated on the basis of changes in rheological and filtration parameters under the influence of a temperature of 160 °C. Attempts were made to increase the thermal resistance of drilling fluids by using antioxidants and glycol compounds. The effectiveness of increasing the thermal resistance of muds by adding synthetic polymers, nanomaterials, and graphite was tested. A new way of increasing the thermal resistance of drilling muds by using fatty amine compounds in combination with the amine agent ‘TEA’ was proposed. Tests showed that the addition of polyglycol and the antioxidant agent sodium ascorbate to the mud did not protect the polymers from decomposition at 160 °C. There was no effect of increasing the thermal conductivity on improving the thermal resistance of the scrubber. Based on the analysis of results from laboratory tests, a composition of a water-based drilling mud without bentonite was developed for drilling geothermal wells. The developed drilling mud is characterized by thermal resistance up to 160 °C, stable rheological parameters, low filtration, and appropriate thermal conductivity characteristics.