As a result of almost three-year observations conducted in the fault zone in the Beshtau magmatic massif area (Caucasian Mineral Waters), anomalous seasonal fluctuations in radon exhalation rate were registered. Seasonal fluctuations are characterized by highs in summer and lows in winter. Summer values reached 23800 mBq/(m2s), while in winter the radon exhalation rate decreased to 40 mBq/(m2s). Radon exhalation rate in the fault zone shows a clear direct correlation with air temperature. The rise of radon levels in spring and fall in autumn are timed to the moments when the temperature of the atmospheric air becomes, respectively, above and below the temperature of the rock massif. It is established that seasonal fluctuations of radon levels are caused by changes in the direction of convective radon transport in the fractured zones. The obtained data suggest that the formation of seasonal radon anomalies in the fault zones is due to the circulation of atmospheric air in permeable zones of the rock massif, which occurs due to the temperature difference between the massif and the atmosphere.