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Potential evapotranspiration (<i>ET</i>₀) is an essential component of the hydrological cycle, and quantitative estimation of the influence of meteorological factors on <i>ET</i>₀ 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 <i>ET</i>₀. 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 <i>ET</i>₀ to identify the mechanisms underlying changing <i>ET</i>₀ rates. The results showed that the average <i>ET</i>₀ for the Yanhe River Basin, China from 1978–2017 was 935.92 mm. Save for a single location (Ganquan), <i>ET</i>₀ 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 <i>ET</i>₀ 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 <i>ET</i>₀ increase in the basin. The predominant factor driving increasing <i>ET</i>₀ was rising air temperatures, but this too varied significantly by location and time (intra- and interannually). Decreasing wind speed at Ganquan Station decreased <i>ET</i>₀ by −9.16%, and was the primary factor underlying the observed, local “evaporation paradox”. Generally, increase in <i>ET</i>₀ was driven by air temperature, wind speed and solar radiation, whereas decrease was derived from relative humidity.