Urban greenspace is an effective strategy to mitigate the urban heat island (UHI) effect. While its cooling effects are well-established, uncertainties remain regarding the combined impact of internal and external landscape patterns, particularly the role of morphological spatial patterns. Taking 40 urban greenspaces in Wuhan as the sample, this study quantified cooling effects from maximum and accumulative perspectives and investigated the impacts of internal and external landscape patterns. First, using land surface temperature (LST) data, four cooling indexes—greenspace cooling area (GCA), cooling efficiency (GCE), cooling intensity (GCI), and cooling gradient (GCG)—were quantified. Then, the relationships between these indexes and landscape patterns, including scale and landscape composition, morphological spatial pattern, and surrounding environmental characteristics, were investigated by correlation analysis and multiple stepwise regression. The results showed that the cooling effects of greenspace varied across different perspectives. Both greenspace area and perimeter exerted non-linear impacts on cooling effects, and morphological spatial pattern significantly influenced cooling effects. Core proportion was positively correlated with cooling effects, with an optimal threshold of 55%, whereas bridge and branch proportions had negative impacts. External landscape patterns, particularly the proportion of impervious surfaces and building coverage, also affected cooling effects. Additionally, cluster analysis using Ward’s system clustering method revealed five cooling bundles, indicating that urban greenspaces with diverse cooling needs exhibited different cooling effects. This study offers valuable insights for optimizing urban greenspace design to enhance cooling effects and mitigate UHI.