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The urban heat island is considered as one of the most important climate change phenomena in urban areas, which can result in remarkable negative effects on flora, concentration of pollutants, air quality, energy and water consumption, human health, ecological and economic impacts, and even on global warming. The variation analysis of the surface urban heat island intensity (SUHII) is important for understanding the effect of urbanization and urban planning. The objective of this study was to present a new strategy based on the Shannon's entropy and Pearson chi-square statistic to investigate the spatial and temporal variations of the SUHII. In this study, Landsat TM, ETM+, OLI and TIRS images, MODIS products, meteorological data, topographic and population maps of the Babol city, Iran, from 1985 to 2017, and air temperature data recorded by ground recorder devices in 2017 were used. First, Single-Channel algorithm was used to estimate land surface temperature (LST), and the maximum likelihood classifier was employed to classify Landsat images. Then, based on LST maps, surface urban heat island ratio index was employed to calculate the SUHII. Further, several statistical methods, such as the degree-of-freedom, degree-of-sprawl and degree-of-goodness, were used to analyse the SUHII variation along different geographic directions and in various time periods. Finally, correlation between various parameters such as air temperature, SUHII, population variation and degree-of-goodness index values were investigated. The results indicated that the SUHII value increased by 24% in Babol over different time periods. The correlation coefficient yielded 0.82 between the values of the difference between the mean air temperature of the urban and suburbs and the SUHII values for the geographic directions. Furthermore, the correlation coefficient between the population variation and the degree-of-goodness index values reached 0.8. The results suggested that the SUHII variation of Babol city had a high degree-of-freedom, high degree-of-sprawl and negative degree-of-goodness.