The amplitude of diurnal variations in atmospheric air temperature may exceed 25 °C depending on the climatic zone and season. This gives rise to unsteady heat-transfer processes in downcast mine shafts and in the subsequent underground workings along the airflow path. The present study focuses on investigating the damping effect of the amplitude of diurnal fluctuations in the thermodynamic parameters of atmospheric air in downcast shafts of potash mines. The thermal damping effect consists in the attenuation of air temperature fluctuation amplitude as the airflow moves down the shaft due to heat exchange with the shaft lining and mass-transfer processes. A combined theoretical and experimental approach is proposed to predict air microclimate parameters at the junction of a downcast shaft with an underground level using a conjugate convective-diffusive heat and mass transfer model that accounts for processes in the shaft air, the lining, and the surrounding rock mass. A methodology for conducting in situ measurements at the study sites is described, the necessary experimental and calculation parameters are provided, and field measurement data obtained for two downcast shafts of potash mines with different depths are presented. The experimental data were used to validate the proposed model. The agreement between measured and calculated results confirms the suitability of the selected model for predicting air temperature at the shaft-underground level junction. Effective heat-transfer coefficients between the airflow and the shaft wall were determined for both downcast shafts, along with effective thermal diffusivities of the surrounding rock mass. An empirical relationship was established for the air temperature in the shaft bottom chamber of the underground level as a function of the daily mean temperature, the amplitude of surface temperature fluctuations, and the shaft depth.