The mitigation effects of park green space on Urban Heat Island (UHI) have been extensively documented. However, the relative effects of the configuration of park components on land surface temperature (LST) inside the park and indicators (i.e., park cooling intensity and distance) surrounding the park is largely unknown. Therefore, the main objective of this study is to explore the quantitative impacts of configuration and morphology features under different urban park scales on the cooling effect. In this study, based on Landsat-8 OLI/TIRS images on 3 August 2015 and 16 August 2020 during summer daytime, the LSTs of Shanghai City were retrieved by atmospheric correction method. Then, the relationships of park landscape features with LSTs in the park and typical indicators representing cooling efficiency of 24 parks on different grades were analyzed. The results showed that the average temperature in urban parks was, respectively, 1.46 °C and 1.66 °C lower than that in the main city of Shanghai in 2015 and 2020, suggesting that urban parks form cold islands in the city. The landscape metrics of park area (PA), park perimeter (PP), green area (GA) and water area (WA), were key characteristics that strong negatively affect the internal park LSTs. However, the park perimeter-to-area ratio (PPAR) had a significant positive power correlation with the park LSTs. Buffer zone analysis showed that LST cools down by about 0.67 °C when the distance from the park increases by 100 m. The Maximum Cooling Distance (MCD) for 2015 and 2020 had a significant correlation with PA, PC, PPAR, GA and WA, and increased sharply within the park area of 20 ha. However, the medium park group had the largest Maximum Cooling Intensity (MCI) in both periods, followed by the small park group. There could be a trade-off relationship between the MCD and MCI in urban parks, which is worth pondering to research. This study could be of great significance for planning and constructing park landscapes, alleviating Urban Heat Island effect and improving urban livability.