Monthly mean daily maximum temperature for the Australian continent between 1976-2005. Daily maximum temperature regulates rates of plant growth. Modelled by fitting trivariate thin plate smoothing spline functions of longitude, latitude and vertically exaggerated elevation to observed and estimated monthly 1976-2005 daily maximum temperature means at 1541 Bureau of Meteorology stations. Missing monthly temperature values were estimated by regression with the long term station that provided estimates of the 1976-2005 monthly means with with the least standard error. This was applied to each station with at least 5 years of record between 1921 and 2012. Quality controls were applied to the regression and the surface fitting processes to remove poor quality data. Thus, of 1597 stations with at least 5 years of record, 38 stations had poor regressions with long term stations and a further 18 stations had extreme studentised residuals from initial spline analyses. These were commonly stations with an old or short period of record, or with an imprecise location. The spline analysis also incorporated the impact of distance from the coast as provided by eMAST_ANUClimate_fx_dist_v1m0. The root mean square error of individual cross validation residuals provided by the spline analysis at 225 stations with near complete records, of at least 28 years, is 0.47 degrees Celsius. The incorporation of distance from the coast reduced overall cross validation errors by around 10%. A comprehensive assessment of the analysis and the factors contributing to the quality of the final interpolated monthly mean daily maximum temperature grids is in preparation.