Low-temperature processed ITO thin films offer the potential of overcoming the doping limit by suppressing the equilibrium of compensating oxygen interstitial defects. To elucidate this potential, electrical properties of Sn-doped In₂O₃ (ITO) thin films are studied in dependence on film thickness. In-operando conductivity and Hall effect measurements during annealing of room temperature deposited films with different film thickness in different environments allow to discriminate between the effects of crystallization, grain growth, donor activation and oxygen diffusion on carrier concentrations and mobilities. At 200 °C, a control of carrier concentration by oxygen incorporation or extraction is only possible for very thin films. The electrical properties of thicker films deposited at room temperature are mostly affected by grain size. The remaining diffusivity of compensating oxygen defects at 200 °C is sufficient to screen the high Fermi level induced by deposition of Al₂O₃ using atomic layer deposition (ALD), which disables the use of defect modulation doping at this temperature. The results indicate that achieving higher carrier concentrations requires a control of the oxygen pressure during deposition in combination with seed layers to enhance crystallinity or the use of near room temperature ALD.