This paper deals with the analysis of the MET Office Hadley Centre's sea surface temperature data set (HadSST3) by using long-range dependence techniques. We incorporate linear and segmented trends using fractional integration, and thus permitting long memory behavior in the detrended series. The results indicate the existence of warming trends in the three series examined (Northern and Southern Hemispheres along with global temperatures), with orders of integration which are in the range (0.5, 1) and thus implying nonstationary long memory and mean reverting behavior. This is innovative compared with other works that assume short memory behavior in the detrended series. Allowing for segmented trends two features are observed: increasing values in the degree of dependence of the series across time and significant warming trends from 1940 onwards.