Blue-green spaces are essential for mitigating urban heat islands. The matching between their supply and demand affects the fairness and effectiveness of urban cooling facilities. This study focuses on the third ring area of Urumqi, Xinjiang, China. Cooling supply indicators and cooling demand indicators for blue-green spaces are established. Using coupling coordination and bivariate spatial autocorrelation models, it evaluates the cooling supply-demand relationship during 2010-2020. Results show that: (1) There is a "suburban cold sources dominated, urban supply turned positive" pattern in the cooling supply of Urumqi's blue-green spaces. (2) Cooling demand has a significant "dual-core spatial separation". The physical demands are concentrated in the high-temperature patches around the city, while the social demands are mainly distributed in the core area of the urban district. (3) There is a severe supply-demand spatial mismatch, with extremely low coupling coordination. The core issue is that high-supply cropland cold sources are far from the high-social-demand urban area. This study provides an important scientific basis for formulating effective cooling strategies for oasis cities through the analysis of the supply and demand matching of blue and green space. It uniquely helps safeguard ecological security and residents' health in arid-zone cities.