This paper numerically studies the thermal performances of electroosmotic flow (EOF) in a symmetric Y-shaped microchannel heat sink (MCHS) having a constant total channel surface area, that is, constant convective heat transfer area. It is found that the average convective heat transfer coefficient of EOF increases with the increasing driven voltage, which is attributed to the increase of EOF flowrate with the increasing driven voltage. However, the maximum MCHS temperature shows an increasing after decreasing trend with the driven voltage owing to the dramatically increasing Joule heating when the voltage is large enough. Further, both the maximum MCHS temperature and average convective heat transfer coefficient are sensitive to the cross-sectional dimensions of the Y-shaped microchannels. The thermal performances of EOF in the Y-shaped MCHS show a strengthening to weakening trend with the increasing daughter-to-parent channel diameter ratio of the Y-shaped microchannel with circular cross-sectional shape, and show a similar strengthening to weakening trend with the increasing daughter-to-parent channel width ratio and the increasing microchannel height of the Y-shaped microchannel with rectangular cross-sectional shape. These cross-sectional dimension dependences of thermal performances are related to the increasing to decreasing trend of EOF flowrate changing with the microchannel cross-sectional dimensions.