An important requisite in any water resources management program is the knowledge of the natural processes that regulate the hydrological cycle, especially for spatial and temporal analyses of these processes. This work aimed to explore spatial and temporal trends of reference evapotranspiration (ETo), evaluate ETo variation dynamics and quantify the contribution of each one of the meteorological variables in ETo calculation in the São Francisco River basin. Daily data of maximum and minimum air temperature, mean relative air humidity, wind speed and net radiation from 101 weather stations, for the period from 1961 to 2015, were used and are part of the network of the National Institute of Meteorology (INMET). Climate trend analysis was performed using the non-parametric Mann-Kendall statistical test and the sensitivity analysis for the Penman-Monteith equation was carried out based on partial derivatives as a function of the key meteorological variables of ETo (air temperature, net radiation, wind speed and actual water vapor pressure). A significant increase (p<0.01) in vapor pressure deficit (VPD) associated with the increase in mean air temperature contributed to increments in ETo along the studied period. The scenario in the entire São Francisco River basin is of increase in the values of the climatic variables, particularly evapotranspiration (85% of basin area with increments) and rainfall (52% of basin area with decrements). Results indicate an increase in ETo variation rates of approximately 2.424 mm year-2, on average, in the entire basin. The energy term represents higher weight in ETo calculation in 81% of the basin territory.