Energy building design today aims to ensure thermal comfort and indoor air quality; this concern has been increased, given the recent SARS-CoV-2 pandemic. The proposed work investigates the effect of increased natural ventilation on energy requirements, ensuring low CO2 levels and acceptable Indoor Air Quality (IAQ) in general. The case of hospitals was chosen because of the stringent IAQ requirements they raise as a result of the burdened (physical, chemical, biological) indoor environment, as well as the vulnerable health of the patients. The current energy analysis was carried out in patient wards, waiting rooms, and operating rooms. The proposed correlation between IAQ and energy is infrequent in the relevant literature, especially for the case of hospitals. Different scenarios regarding the ventilation mode are examined, including pure natural ventilation, natural ventilation combined with air cleaners, as well as mechanical ventilation. According to the results, improvement of the air quality leads to higher energy demand; this is the case of mechanical ventilation, noting that not properly designed natural ventilation techniques may lead to high energy consumption, without ensuring acceptable IAQ. Air cleaners can contribute towards better environment, potentially decreasing ventilation requirements; the issue of fresh air adequacy has to be examined though. The demonstrated methodological analysis and results can help the designer to investigate the efficiency of different ventilation modes, involving the effect of thermal envelope, geometrical and operation parameters, towards the energy requirements minimization and IAQ quality maximization.