[en] The multifractal structure of global monthly mean temperature anomaly time series over the period 1850–2012 are studied in terms of the multifractal detrended moving average (MFDMA) analysis. We try to address the possible source(s) and the nature of multifractality in the time series data by comparing the results derived from the actual series with those from a set of shuffled and surrogate series. It is seen that the MFDMA method predicts a multifractal structure of the temperature anomaly records that is more or less similar to what was obtained from the multifractal detrended fluctuation analysis (MFDFA) for the same set of data. In our analysis the major contribution of multifractality in the data is found to be due to the long-range temporal correlation among the measurements, although the contribution of a fat-tail distribution function of the variables is not negligible. The existence of a long-range correlation is also confirmed by the constancy of the local slopes of the fluctuation function over a sufficient scale interval. The results of the moving average analysis are found to depend upon the location of the detrending window and tend to the observations of the MFDFA for a specific choice of the location of the detrending window. (paper: classical statistical mechanics, equilibrium and non-equilibrium)