The gas-dynamic and heat-exchange behaviours of air flows in gas-dynamic systems have a significant impact on the efficiency and environmental performance of most technical equipment (heat engines, power plants, heat exchangers, etc.). Therefore, it is a relevant task to obtain reliable experimental data and physical laws on the influence of cross-sectional shape and initial turbulence intensity on gas dynamics and the level of heat transfer. In this study, data were experimentally obtained on the instantaneous values of the local velocity and local heat transfer coefficients of stationary air flows in straight pipes with circular, square, and triangular cross-sections at different initial values of the turbulence intensity. The measurements were carried out with a constant temperature hot-wire anemometer, thermocouples, and pressure sensors. Based on the research results, data on the turbulence intensity and averaged local heat transfer along the length of pipes with different cross-sections were summarised. It has been established that turbulence intensity in a square pipe is up to 40% higher than in a round channel; in a triangular channel, on the contrary, it is up to 28% lower. After the air flow’s initial turbulence, the relaxation of the flow in square and triangular pipes occurs faster than in a round channel. It is found that the initial intensity of turbulence leads to an increase in the averaged local heat transfer, which is typical of all investigated pipe configurations and initial conditions.