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Urban trees cool their environment by transpiration (latent heat flux, LE) and shading, modifying thereby the energy budget and alleviating urban heat. However, the cooling effect from LE may be critically reduced during heatwaves, when trees reduce stomatal conductance (gS) to prevent hydraulic dysfunctions. Recent advances in our understanding of stomatal behaviour under high temperatures indicate that gS may still be maintained during extreme heat to allow canopy cooling, but implications for urban heat stress mitigation remain elusive. We continuously recorded sap flow on eight Platanus x acerifolia trees in Geneva to assess LE and canopy conductance (GAsw) during the summer of 2023, which was characterised by two record-breaking heatwaves. We further repeatedly assessed leaf water potentials at pre-dawn and midday (Ψpre, Ψmid), stomatal conductance (gS), and leaf, canopy, and ground surface temperatures in shaded and sunlit parts around the trees (Tleaf, Tcan, Tsurf). Using the ecohydrological model UT&C, we determined the total energy budget of the urban square, and assessed whether LE predictions match empirical measurements during heatwaves. We found that despite prolonged heatwaves with air temperature (Tair) reaching 39.1 ºC, trees were only marginally water stressed, with Ψmid mostly above -1.7 MPa, and continued transpiring throughout the day up to 37.1 kg h-1 (i.e. LE of 25.3 kW). Despite reduced GAsw measured LE was similar during heatwaves (i.e., Tair> 30 ºC) as during cooler periods and accounted for approximately 34 % of the urban heating by incoming solar radiation (Q*) throughout the season. In contrast, LE model predictions showed a marked decrease of urban cooling during heatwaves, thereby underestimating actual tree transpiration cooling. Despite unprecedentedly high Tair during two summer heatwaves, trees maintained high transpiration, and thereby efficiently cooled the urban environment. Measured LE at Tair above 30 ºC surpassed model estimations due to continued tree transpiration. Consequently, actual cooling effects of urban trees during heatwaves might be considerably underestimated by current model predictions. Cities with intermittent heatwaves may thus continue to rely on effective vegetation cooling by transpiration.