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The assessment of regional climate and hydrological impacts at different levels of global‐mean temperature increase became vital to guide decision makers and water management planners after the adoption of the Paris Agreement in 2015. With current emission trends close to a pathway of 3 °C warming by the end of the present century, this study investigates the projected regional hydrology impacts over La Plata basin (LPB) for the warming thresholds of 1.5 and 2 °C established in Paris and for 3 °C above the pre‐industrial level. We also explore the consequences from following a medium or high‐emission representative concentration pathway (RCP) to achieve the different warming targets. In order to determine the possible changes in precipitation, evapotranspiration, runoff and river discharges, we use the variable infiltration capacity (VIC)‐distributed hydrology model in combination of bias‐corrected GCM outputs from the Inter‐Sectorial Impact Model Intercomparison Project phase 2a (ISIMIP). Because the behaviour of the hydrometeorological variables is not homogeneous over LPB, we analysed impacts of the different changes in mean global temperature and RCPs over four sub‐basins: Paraguay, Paraná, Iguazú and Uruguay. Overall, most of the changes over the sub‐basins suggest moister conditions with increasing temperatures. The comparison of the RCPs indicates that increases in precipitation, evapotranspiration and runoff would be larger under the medium‐emission scenario. When the different responses of the various components of the terrestrial water cycle were integrated, results show that variation of annual mean streamflow in all sub‐basins ranges between ±20%. However, in most cases, the sign of the changes highly depends on the RCP chosen to achieve a warming level.