In museums, poor microclimate conditions, especially large changes in relative humidity and temperature, can lead to serious deterioration of the exhibits. Properly designed heating, ventilation, and air conditioning (HVAC) systems for precise control of the air parameters are required. However, due to the financial restrictions of museums, complex air-conditioning systems are often not feasible. In this study, we tested and propose novel methods to reduce the short- and long-term fluctuations in the relative humidity in exhibition rooms of a Polish museum. The methods only include indoor temperature and ventilation airflow control strategies, without the use of (de)humidification equipment. The analysis is based on simulations using EnergyPlus software. A multi-zone thermal model of the museum building was validated and calibrated with measured data. A full calendar year was simulated for five control cases (including the current method used) and two internal heat gain schedules. The energy demand for heating and cooling for each case was calculated. The combination of temperature control and adequate ventilation using ambient airflow allows for dramatic improvement in the microclimate conditions. The proportion of the year when the instantaneous indoor relative humidity is ±5% from set point decreased from 85% to 20%. A significant effect was obtained over the summer months.