Accurate air temperatures underpin environmental research. Most professional meteorological air temperature measurements still expose thermometers within traditional, naturally ventilated screens. Their representation of true air temperature depends on screen airflow, and therefore local winds. Accuracies of daily maximum (Tmax) and minimum (Tmin) air temperatures are assessed by comparison between a naturally ventilated large conventional screen and a co‐located aspirated reference screen. In over 1200 days' data, the naturally ventilated Tmin and Tmax both showed small (median < 0.06°C) cold bias, but, in 1% of cases, warm Tmax bias and cold Tmin bias >|1°C|. The Tmin cold bias is associated with calm clear nights, and the Tmax warm bias events with calm winter days at low sun angles, allowing solar heating of the screen. The prevalence of poor natural ventilation, potentially affecting Tmin and Tmax, is estimated across European sites. Poor ventilation occurred at Tmin for 12% of values, and at Tmax for 4%. Climatological averaging will reduce these effects, but, without corroborating wind data, statistical changes in Tmin or Tmax, including identifying “Tropical Nights” (Tmin > 20°C) or occurrences of winter extremes, may have limited value. Wider adoption of aspirated thermometer screens, with an initial overlap period, will largely eliminate these effects.