CHIRTSmax is a monthly 0.05 degree semi-global (60S-70N) gridded dataset describing monthly averages of daily maximum 2m air temperatures (Tmax). The CHIRTSmax combines three separate components: 1) a static high resolution (0.05) background Tmax climatology describing average 1981-2010 air temperature conditions at each location, 2) time-varying 0.05 degree satellite thermal infrared-based estimates of monthly Tmax anomalies, and 3) time-varying 0.05 degree 2m Tmax anomalies based on interpolated station observations. The thermal infrared-based temperature anomalies are based on sub-daily inter-calibrated geostationary weather satellite observations from the GridSat archive, filtered to reduce cloud contamination. The station data archive is drawn from the Berkeley Earth station data set. For each month and location, the thermal infrared and interpolated station components are blended, based on weights derived from an empirical spatial covariogram and the distance to the nearest station. Grid cells near stations will favor the interpolated station data. Values far from stations will be primarily based on the satellite temperature fields. These blended anomaly fields are added to the Tmax climatology to produce the CHIRTSmax fields. For details, please see Funk et al. 2019.