Computational fluid dynamics models have been developed to predict airborne exposure to the SARS‐CoV‐2 virus from a coughing person in a mechanically ventilated room. The models were run with three typical indoor air temperatures and relative humidities (RH). Quantile regression was used to indicate whether these have a statistically significant effect on the airborne exposure. Results suggest that evaporation is an important effect. Evaporation leads to respiratory particles, particularly those with initial diameters between 20 and 100 μm, remaining airborne for longer, traveling extended distances and carrying more viruses than expected from their final diameter. In a mechanically ventilated room, with all of the associated complex air movement and turbulence, increasing the RH may result in reduced airborne exposure. However, this effect may be so small that other factors, such as a small change in proximity to the infected person, could rapidly counter the effect. The effect of temperature on the exposure was more complex, with both positive and negative correlations. Therefore, within the range of conditions studied here, there is no clear guidance on how the temperature should be controlled to reduce exposure. The results highlight the importance of ventilation, face coverings and maintaining social distancing for reducing exposure.