Potential evapotranspiration (ET0) is an essential component of the hydrological cycle, and quantitative estimation of the influence of meteorological factors on ET0 can provide a scientific basis for studying the impact mechanisms of climate change. In the present research, the Penman-Monteith method was used to calculate ET0. The Mann-Kendall statistical test with the inverse distance weighting were used to analyze the spatiotemporal characteristics of the sensitivity coefficients and contribution rates of meteorological factors to ET0 to identify the mechanisms underlying changing ET0 rates. The results showed that the average ET0 for the Yanhe River Basin, China from 1978–2017 was 935.92 mm. Save for a single location (Ganquan), ET0 increased over the study period. Generally, the sensitivity coefficients of air temperature (0.08), wind speed at 2 m (0.19), and solar radiation (0.42) were positive, while that of relative humidity was negative (-0.41), although significant spatiotemporal differences were observed. Increasing air temperature and solar radiation contributed 1.09% and 0.55% of the observed rising ET0 rates, respectively; whereas decreasing wind speed contributed -0.63%, and relative humidity accounted for -0.85%. Therefore, it was concluded that the decrease of relative humidity did not cause the observed ET0 increase in the basin. The predominant factor driving increasing ET0 was rising air temperatures, but this too varied significantly by location and time (intra- and interannually). Decreasing wind speed at Ganquan Station decreased ET0 by -9.16%, and was the primary factor underlying the observed, local “evaporation paradox.” Generally, increases in ET0 were driven by air temperature, wind speed and solar radiation, whereas decreases were derived from relative humidity.