The quality of the classroom environment, including ventilation, air quality and thermal conditions, has an important impact on children’s health and academic achievement. The use of portable HEPA filter air cleaners is widely suggested as a strategy to mitigate exposure to particulate matter and airborne viruses. However, there is a need to quantify the relative benefits of such devices including the impacts on energy use. We present a simple coupled dynamic thermal and air quality model and apply it to naturally ventilated classrooms, representative of modern and Victorian era construction. We consider the addition of HEPA filters with, and without, reduced opening of windows, and explore concentrations of carbon dioxide (CO2), particulate matter PM2.5, airborne viral RNA, classroom temperature and energy use. Results indicate the addition of HEPA filters was predicted to reduce PM2.5 by 40–60 % and viral RNA by 30–50 % depending on the classroom design and window opening behaviour. The energy cost of running HEPA filters is likely to be only 1 %–2 % of the classroom heating costs. In scenarios when HEPA filters were on and window opening was reduced (to account for the additional clean air delivery rate of the filters), the heating cost was predicted to be reduced by as much as − 13 %, and these maximum reductions grew to − 46 % in wintertime simulations. In these scenarios the HEPA filters result in a notable reduction in PM2.5 and viral RNA, but the CO2 concentration is significantly higher. The model provides a mechanism for exploring the relative impact of ventilation and air cleaning strategies on both exposures and energy costs, enabling an understanding of where trade-offs lie.