We report measurements of the electron dephasing time extracted from the weak localization (WL) correction to the average conductance in an open AlGaAs/GaAs quantum dot from 1 K to 13 mK. In agreement with theoretical predictions but in contrast with previous measurements in quantum dots, the extracted dephasing time does not saturate at the lowest temperatures. We find that the dephasing time follows an inverse linear power law with temperature. We determine that the extraction of the dephasing time from WL is applicable down to our lowest temperatures, but extraction from finite magnetic field conductance fluctuations is complicated by charging effects below 13 mK.