Heat storage in systems integrated with renewable energy sources in facilities can reduce the consumption of fossil fuels, cut maintenance costs, and decrease greenhouse gas emissions from buildings and other objects. One of the possible solutions is the use of a stone heat accumulator for short-term heat storage and the use of this deposit in the ventilation process of the facility. During short-term air flow through the porous material from which an accumulator bed is made, there is an exchange of heat and mass between the flowing air and the bed particles. In the long term, the use of an accumulator can lead to an increase in dust and the development of pathogenic microorganisms, endangering human life and health. Therefore, understanding the factors influencing the efficient use of a stone deposit is very important. The aim of this study is to calculate the changes in thermal-mass parameters in the air flowing out of the stone accumulator and to assess the effect of long-term stone accumulator use on the content of microorganisms and dust concentration in bioaerosol. The application of the heat storage system in the stone bed leads to the formation of strictly controlled microclimatic conditions, and the tested air does not constitute a threat to the people staying in the object. The concentration standards of PM10 and PM2.5 exceeded the limit values (PM2.5 = 20 μg∙m−3 and PM10 = 40 μg∙m−3), and, thus, the air in the studied greenhouse was classified as polluted. The analysis also showed that, for the analyzed conditions, a 20% increase in the initial temperature of the accumulator bed results in a nearly 20% increase in the outlet air temperature.