If standard error of station mean temperature is say 0.1 degC, then
divide by square root of no. of stations, so 100 stations give 0.01
degC. Probably not worth giving more accuracy because of possible
bias due to changes in thermometer calibration and observing
practices, and locations of stations. I hope that the climate
scientists have considered this, and that any bias over the years is
~0.01 rather than ~0.1 degC.
Keith Grant