Abstract Air temperature measurements in naturally ventilated thermometer screens underpin the instrumental climate record. Increasing automation is, however, revealing limitations. One is through thermometer time response, especially in light winds or calm conditions, often at the daily temperature minimum. The exponential time response τ63 ${\tau }{63}$ for thermometers enclosed within a Stevenson screen is a key parameter, but poorly known. Here, τ63 ${\tau }{63}$ is evaluated in a practical experimental situation against the World Meteorological Organization (WMO)’s recommended sensor τ63≤20 ${\tau }{63}\le 20$ s. We find τ63 ${\tau }{63}$ increases with sensor diameter d $d$, with only a d $d$ = 2 mm sensor meeting WMO expectations, even then requiring ambient wind speeds ≥3ms−1 ${\ge} 3\,\mathrm{m}{\mathrm{s}}^{-1}$. Typical d $d$ = 4 mm sensors never meet the criterion when either force‐ or naturally ventilated, with τ63≥20 ${\tau }{63}\ge 20$ mins in a naturally ventilated arrangement under calm conditions. Inadequate τ63 ${\tau }{63}$ will lead to underestimation of the diurnal temperature range or other local measures derived from daily temperature maxima and minima.