This paper presents a global air and sea temperature anomalies analysis based upon a combination of the wavelet multiresolution analysis and the scaling analysis methods of a time series. The wavelet multiresolution analysis decomposes the two temperature signals on a scale-by-scale basis. The scale-by-scale smooth and detail curves are compared and the correlation coefficients between each couple of correspondent sets of data evaluated. The scaling analysis is based upon the study of the spreading and the entropy of the diffusion generated by the temperature signals. Therefore, we jointly adopt two distinct methods: the Diffusion Entropy Analysis (DEA) and the Standard Deviation Analysis (SDA). The joint use of these two methods allows us to establish with more confidence the nature of the signals, as well as their scaling, and it yields the discovery of a slight Levy component in the two temperature data sets. Finally, the DEA and SDA are used to study the wavelet residuals of the two temperature anomalies. The temporal regions of persistence and antipersistence of the signals are determined and the non-stationary effect of the 10-11 year solar cycle upon the temperature is studied. The temperature monthly data cover the period from 1860 to 2000 A.D.E.