Studying the non-stationarity of extreme precipitation and its response to temperature can help the fight against the negative effects from rainfall-related hazards. Based on the grid dataset of daily precipitation and temperature over the Yangtze River Basin from 1961 to 2020, the generalized extreme value models are established to confirm whether the previous 0-day (T0) and the previous 9-day (T1-9) local average temperatures would cause non-stationarity in extreme precipitation. Then the responses of extreme precipitation to T0 and T1-9 are investigated by equal sample binning method, piecewise linear regression and exponential regression. The results showed that the extreme precipitation was non-stationary at 99.7% of the grids of the basin, T0 and T1-9 induced non-stationarity in extreme precipitation at 74.4% of the grids, and T1-9 had a greater impact on extreme precipitation than T0. Extreme precipitation intensity increased at low temperature but decreased at high temperature (peak structure) with the rise of T0 in the basin. Besides, there was an obvious dividing line at the eastern margin of the Tibetan Plateau, and the peak-point temperature was higher (about 24℃) in the east but lower (about 9℃) in the west of this line. Meanwhile, the scaling rate of extreme precipitation with T0 range from -12.3%/℃ to 53.6%/℃ and showed a “super-CC, CC-like and sub-CC scaling” pattern from Sichuan Basin center to the surrounding areas. Extreme precipitation intensity with increasing T1-9 mainly showed an upward trend in the west while peak structure in the east-central region of the basin, and the intensity of the heaviest extreme precipitation reached its peak when the temperature was close to 25 ℃. Furthermore, the scaling rate of extreme precipitation with T1-9 roughly exhibited a pattern of super-CC to CC-like to sub-CC scaling from west to east over the basin, and the scaling rate fell within a range of -3.7%/℃ to 33.8%/℃, which was mainly concentrated in the vicinity of 4%/℃ and 10%/℃. With the increase of precipitation intensity, the range of scaling change shortened owing to the decrease of sensitivity of extreme precipitation to temperature change. In addition, it was speculated that the super-CC scaling could result from convective precipitation, latent heat release and so on, and the peak structure could be related to cooling effect of precipitation, anticyclonic activities, etc.