In this study, we examined changes in EEG signals during the cognitive activity at different air temperatures and relative humidities (RH). Thirty-two healthy young people acclimatized to the subtropical climate of Changsha, China, were recruited as subjects. They experienced four air temperature levels (26, 30, 33, and 37 °C) and two relative humidity levels (50 and 70%) in a climate chamber. During 175 min-long exposures to each thermal condition, they performed cognitive tasks and their EEG signals were measured. Relative humidity of 70% and increased temperature at this relative humidity significantly increased the relative power of δ-band and significantly decreased relative power of θ-band, α-band, and β-band. This may suggest that subjects were more sleepy but less drowsy, and it was more difficult for them to think clearly. At the same time, subjective evaluations indicated that they could be less alert and it was harder for them to think. However, no changes in performance of tasks measuring cognitive abilities were observed. It remains therefore unclear whether EEG can be a credible marker of changes in cognitive activity as a result of changes in indoor environmental quality in buildings and the future experiments should closely examine this issue.