Urban parks serve as vital nature-based solutions for alleviating urban heat. Most studies have treated parks as whole entities, underlining their cooling spillover to surrounding areas, yet systematic quantification of cooling gradients within parks remains limited. Here, using Landsat-derived land surface temperature (LST) data and other remote sensing data, we proposed a "buffer-function fitting" framework to evaluate intra-park surface cooling effects across 58,957 parks in 709 cities worldwide, spanning different climate zones and continents. We further identified the key drivers and response thresholds from four dimensions: park morphology, internal park landscape, surrounding buffer landscape, and background climate. Our results indicate that 74% of global urban parks function as cool-core parks, with LST decreasing from the park boundary toward the interior. The global mean intra-park surface cooling intensity (IPCIs), measured as the fitted LST difference between the boundary and the innermost buffer, reaches 1.15 K and is stronger in cold and arid zones. 68% of cool-core parks follow an exponential decay pattern for LST gradients, reflecting diminishing marginal effects. Global-scale driver analysis indicates that the IPCIs is primarily controlled by park morphology (accounting for 33%) and internal landscape (29%). The key factors and their corresponding thresholds that markedly enhance cooling effects are park area (> 4.65 ha), mean internal NDVI (> 0.60), and tree cover (> 0.59). Our study fills a critical gap by providing a comprehensive and global-scale understanding of intra-park surface cooling, offering scientific guidance for optimizing park design and advancing climate-resilient urban development.