This research is the first attempt to decipher the effect of PM composition on public health and historical artefacts, in correlation with the monitoring of the daily and seasonal microclimate inside and outside the Roman Mosaic Edifice area. The aim of this study was to investigate the indoor and outdoor conditions of the Roman Mosaic Edifice by several parameters: temperature, apparent temperature (AT), relative humidity (RH), and particulate matter composition. The novelty of this study is highlighted by the multitude of reported data (indoor and outdoor) with direct correlations between climatic factors and PM chemical composition, which has a direct influence on artwork in the museum and on visitor’s health. The particulate matter analyses showed variability related to indoor microclimate conditions as well as to outdoor, coastal anthropic activities. The FTIR and ICP-MS techniques, used for the investigation of PM2.5–10 samples, revealed high concentrations of Fe, Al-rich, and soluble particles inside the investigated museum area. The high values of the measured RH in outdoor areas (99% in the monitoring process in the autumn of 2018 and spring of 2019, and over 50% in the indoor area in all seasons), correlated with the temperature and influenced the chemical composition of PM2.5–10 samples. A strong relationship was found between Cr, Ni, Cu, Cd, and Pb concentrations, temperature, and AT inside the Roman Mosaic Edifice area. On the other hand, a high correlation was found between Al concentrations, temperature, and AT. A low correlation was observed between Al concentrations, temperature, and AT in the outdoor area of the Roman Mosaic Edifice as well as a high correlation between Mn and Cu concentrations, temperature, and AT. In this respect, a strong relationship was remarked between Cr, Fe, Ni, Zn, Cd, and Pb concentrations, temperature, and AT inside the investigated area. The order of the metals analyzed in terms of their abundance in the cold seasons (i.e., autumn and winter, when the temperatures ranged between 0 ◦C and 10 ◦C), inside and outside the investigated area, were found be the same. However, the rise in temperature led to a change in the order of the metals inside the Roman Mosaic Edifice area. The data obtained indicated that as the temperature increases (i.e., in the summer and spring seasons), the Pb concentrations both inside and outside the investigated area are much higher than expected, mainly because of the anthropic activities conducted in the port of Constanta. In conclusion, the final results allowed an estimation of indoor and outdoor air quality, from the point of view of the PM chemical composition, thus giving insight into the health risks for visitors and within the Roman Mosaic Edifice museum space hosted in buildings with natural ventilation.