Sea surface temperature (SST) in the Pacific Ocean is a key component of many global climate models and the El Niño-Southern Oscillation (ENSO) phenomenon. We shall analyse SST for the period November 1981-December 2014. To study the temporal variability of the ENSO phenomenon, we have selected a subregion of the tropical Pacific Ocean, namely the Niño 3.4 region, as it is thought to be the area where SST anomalies indicate most clearly ENSO's influence on the global atmosphere. SST anomalies, obtained by subtracting the appropriate monthly averages from the data, are the focus of the majority of previous analyses of the Pacific and other oceans' SSTs. Preliminary data analysis showed that not only Niño 3.4 spatial means but also Niño 3.4 spatial variances varied with month of the year. In this article, we conduct an analysis of the raw SST data and introduce diagnostic plots (here, plots of variability vs. central tendency). These plots show strong negative dependence between the spatial standard deviation and the spatial mean. Outliers are present, so we consider robust regression to obtain intercept and slope estimates for the 12 individual months and for all-months-combined. Based on this mean-standard deviation relationship, we define a variance-stabilizing transformation. On the transformed scale, we describe the Niño 3.4 SST time series with a statistical model that is linear, heteroskedastic, and dynamical.