Assessing the indoor microclimate of heritage and historic buildings is important to preserve them and their contents and study their decay and damage processes. This study aims to evaluate the thermo-hygrometric environment, and its impact on the exhibited objects and visitors’ comfort of an old Ottoman Palace (Ahmed Bey) converted into a museum. The National Museum of Traditional Arts and Cultural Expressions-Ahmed Bey Palace-is located in Constantine, North East of Algeria, characterized by a semi-arid climate. The building has internal courtyards and does not have an HVAC system. The most critical thermo-hygrometric parameters have been calculated and assessed in the exhibition’s permanents rooms using the HD32.3 datalogger during the winter period from January to March of 2019. The measured data were compared to acceptable values suggested by the Italian Standard UNI 10829 for artefact preservation and to the corresponding external outdoor conditions. The results show that the interior conditions of exhibition rooms are mainly dependent on the external climatic conditions. The air temperature values are out of the acceptable range, while the relative humidity values are higher than the acceptable values. Thus, the monitoring parameters are not reasonably acceptable for the preservation of the kind of objects exhibited and the thermal comfort of visitors.