This paper investigates the heat transfer of airflow in square and circular minichannels. The square channels were machined on the oxygen free copper blocks. The width of them were 0.3, 0.6, 1.0 and 2.0 mm, and the lengths were 10, 20, 50 and 100 mm. The circular channels were drilled in oxygen free copper disks. The diameters of them were 1.0, 1.27, 2.0 and 2.8 mm and the length to diameter ratios were 5 and 10. The mean heat transfer coefficient included the transferee heat upstream of the channel inlet cross-section, since the inlet was not thermally insulated. The pressure ratio of the inlet and outlet plenum was increased up to the flow choked at the channel exit. The square channel showed 7.3 times greater mean heat transfer coefficient than fully developed turbulent pipe flow for width of 2 mm and length of 10 mm channel. The so-called tube cutting method was employed to investigate the sectional heat transfer rate of the square channel. About 75 percent of the total heat transfer was completed in 10 percent inlet portion of the channel. The Stanton number was found to be principally the function of length to diameter ratio. The circular channel showed 6.79 times greater mean heat transfer coefficient than fully developed turbulent pipe flow for diameter of 1.27 mm and length of 6.35 mm channel. The heat transfer coefficient increased as the channel size (width or diameter) became smaller for constant length to diameter ratio. It implied that the result of high heat transfer coefficient had a possibility to be limited to the minichannel. Heat transfer of gas turbine film cooling hole has a possibility to be larger than ever thought.