In modern civil aeroengines, the hot streak and swirl at the exit of the combustor have a significant impact on the aerothermal performance of the high-pressure turbine (HPT). Due to the different design purposes of the combustor and the turbine, hot streak (HS) and swirl (SW) have different spatial distributions at the turbine inlet. This paper conducts a transient simulation of the GE E3 first-stage HPT, considering the swirl and hot streak facing the middle of the passage and the leading edge of the nozzle guide vane, respectively, and also explores the impact of positive and negative swirl. The results show that different clocking positions and swirl directions will change the incident angle and streamline distribution of the vane, thereby affecting the migration of the hot streak, the temperature and the Nusselt number distribution on the stator surface. In positive cases, the hot streak gathers in the upper part of the passage, and in negative cases, it is in the lower part. In middle cases, high-temperature areas appear in both vanes, and the distributions are opposite. Affected by the swirl, when facing the passage center, the pressure side stagnation lines of the two vanes are also different, so the Nusselt number distribution is opposite. When facing the leading edge, only one vane appears. Due to the insensitive interference of the rotor–stator, the transient migration of the hot streak in the rotor is mainly affected by the inherent secondary flow and the temperature at the inlet of the rotor (especially the conditions facing the leading edge), while the upstream residual swirl is less affected. Unlike the middle case, in leading edge cases, the hot streak is separated and needs to be re-mixed before entering the blade passage, so the temperature change in the blade cascade is relatively gentle. Based on this, the Nusselt number distribution on the surface of the blade is similar. In order to obtain the most favorable operating conditions for the engine, the turbine efficiency is used to compare the aerothermal performance under different conditions. Ultimately, it was found that the turbine with the hot streak and positive swirl directly facing the leading edge was the most efficient.