ABSTRACT To accurately determine multi‐centennial trends in climate data records of the Earth's surface temperature, measurements are commonly analysed in the form of anomalies relative to a climatological reference period such as the World Meteorological Organization (WMO) 1961–1990 baseline. One of many climate‐monitoring challenges is that weather records of land surface temperature can be short, typically of the order of several years or decades, and often do not sufficiently overlap the reference period to allow calculation of the climatological normals needed to convert the observations to anomalies. Moreover, the volume of records of this type is increasing due to the rescue of early (pre‐baseline) instrumental paper‐based records and the growing prevalence of newer (post‐baseline) weather stations. To address this, we apply a method to estimate the climatological normal for each calendar month of temperature time series that do not have sufficient data during the baseline period, using an approximation to local expectation kriging with station holdout (LEK). This exploits the information in neighbouring time series to estimate the expected mean level of short series of observations. We apply the method to a global database of monthly land air temperature at 11865 stations based on CRUTEM5 but with the acquisition of an additional 1233 station series including some that extend back to 1781, and with mid‐latitude stations adjusted for exposure bias arising from the transition to Stevenson screens. We evaluate the LEK‐based normals using climatological normals calculated directly from the station observations. Using this method, we obtain estimated normals for 2699 stations that did not previously have normals and we improve the estimated normals for a further 2611 which had previously been estimated from incomplete data. Finally, we demonstrate how incorporating these thousands of previously unused station observation fragments affects hemispheric temperature averages. Pre‐1850 data—primarily from Europe—show a modest warming trend but pronounced multidecadal variability that is greater than after 1850. The additional stations improve spatial coverage by a few percent in recent decades and raise pre‐1860 Northern Hemisphere temperature estimates by approximately 0.1°C.