We have theoretically and experimentally investigated the evolution of the temporal contrast in a 10-PW-level Ti:sapphire laser in the Shanghai Superintense Ultrafast Laser Facility (SULF). The effects induced by the grism pair, spectral shaping filter, and increase in gain on the temporal contrast were investigated. First, it was found that the energy loss of clean seed pulses in the grism pair is a major factor in contrast degradation. Because of the low transmission efficiency of the grism pair (~10%), the temporal contrast is degraded by one order of magnitude. Second, the spectral shaping filter in the regenerative amplifier degrades the temporal contrast by increasing the intracavity loss. Finally, as the amplified spontaneous emission pedestal experiences gain more than the main pulse in Ti:sapphire amplifiers, particularly during saturated amplification, the temporal contrast will further deteriorate as the gain increases in multi-stage Ti:sapphire amplifiers. In addition, the effect on the temporal contrast induced by the extraction during pumping technique in large-aperture Ti:sapphire amplifiers has been considered. According to the investigations described above, the design of the SULF can be further improved. It is predicted that a temporal contrast of over 10-11 can be achieved at a peak power of 10 PW following the improvements. The investigations conducted in this study can provide guidelines for improving the temporal contrast in ultrahigh-peak-power Ti:sapphire lasers.