The electron dephasing processes in two-dimensional homogeneous and inhomogeneous indium tin oxide thin films have been investigated in a wide temperature range 0.3--90 K. We found that the small-energy-transfer electron-electron ($e$-$e$) scattering process dominated the dephasing from a few K to several tens K. At higher temperatures, a crossover to the large-energy-transfer $e$-$e$ scattering process was observed. Below about 1--2 K, the dephasing time $τ_φ$ revealed a very weak temperature dependence, which intriguingly scaled approximately with the inverse of the electron diffusion constant $D$, i.e., $τ_φ (T ≈ 0.3 \, {\rm K}) ∝ 1/D$. Theoretical implications of our results are discussed. The reason why the electron-phonon relaxation rate is negligibly weak in this low-carrier-concentration material is presented. ; Comment: 10 pages, 7 figures