The historic house of Sheikh Mohammed Bin Khalifa, Al Ain (Abu Dhabi, UAE) belongs to the World Heritage Cultural Sites. The courtyard and two rooms include mudbrick archaeological remains that are preserved in showcases for public display. The building lies in a hot desert climate and needs air conditioning to be comfortable. This paper is concerned with indoor showcases and their compatibility with the indoor climate. Sometimes, misting for condensation is generated on the glass panes for the temperature and humidity contrast between the room climate and the showcases that are embedded in the floor. When misting occurs, the remains cannot be viewed. This paper investigates indoor glass misting, the exchanges of heat and moisture between archaeological remains, showcases and rooms, and the results after a year of environmental monitoring. An aim is to assess the potential risks for the preservation of the remains, recognizing the frequency and severity of the conditions for condensation. Another aim is to discuss mitigation methodologies to avoid glass misting, e.g., (i) reducing the room cooling; (ii) raising the glass pane temperature with electrical devices; (iii) increasing air exchanges between showcases and rooms; (iv) adopting a combination of these methodologies.