Thermal remote sensing provides a method to describe spatial heterogeneity of the “urban heat island” effect and to evaluate the function of temperature regulation. Rapid urbanization and heatwave events with increasing frequencies need a quantitative analysis on the supply and demand for an urban temperature regulating service, which is a gap in urban heat island (UHI) studies in rapidly urbanizing cities. In order to study the quantitative relationship between landscape metrics (including area index and shape index) and temperature regulating service, this study applied a temperature regulating service in an urban thermal environment study based on the “source–sink” landscape theory in western Shenzhen in different periods. The identification of source and sink landscapes is based on the spatial relationship of unusual surface features derived from Landsat-5 and -8 and the consideration of the temperature difference. We found that the source landscapes at different periods provide temperature regulating services for different distances, which directly lead to the difference between the theoretical service value based on the Alternative Cost Method and the actual service value considering demand, changing in the same trend. The results show that the supply distance of temperature regulating services in 2005, 2010, and 2013 is 150 m, 180 m, and 210 m, respectively. The temperature regulating service value is 3.043, 3.273, and 4.308 billion yuan in 2005, 2010, and 2013, which is lower than the estimation value without considering supply and demand (16.638, 23.728, and 37.495 billion yuan, respectively). The value of the temperature regulating service has a positive correlation with the increase of the patch area index. With the gradual complexity of the shape, the service value increases first and then decreases. Moreover, the landscapes with the smallest shape index and area index have the shortest distance for service supplying. The assessment of the temperature regulating service needs to consider the presence of demand landscapes. Furthermore, the interaction of landscapes under different conditions requires further consideration. The setting of the cooling landscape shape and area for mitigating the “urban heat island” effect can provide references to urban planners and policymakers in the practice of urban climate adaptation and regulation.