Understanding how climatic variables impact the reference evapotranspiration (ET0) is essential for water resource management, especially considering potential fluctuations due to climate change. Therefore, we used the Sobol method to analyze the spatiotemporal variations of Penman-Monteith ETo sensitivity to the climatic variables: downward solar radiation, relative humidity, maximum and minimum air temperature, and wind speed. The Sobol’s indices variances were estimated by Monte Carlo integration, setting the sample limits to 2.5 and 97.5 percentiles of the daily data of 33 automatic weather stations located in the state of Mato Grosso, Brazil. The results of the Sobol analysis indicate considerable spatiotemporal variations in the sensitivity of ETo to climatic variables and their interactions. The dominant climatic variable responsible for ET0 fluctuations in Mato Grosso is incident solar radiation, which has a more significant impact in humid environments, as observed in the areas of the Amazon biome in the state. Air relative humidity and wind speed have higher sensitivity indices during the dry season in the areas of the Cerrado biome (Savanna) in Mato Grosso. Our findings show that changes in solar radiation, relative humidity, and wind speed cannot be ignored when analyzing changes in reference evapotranspiration.