In this paper, the normalized acoustic input impedance of a narrow pipe with a strong axially non-homogeneous thermal profile subjected to low Mach number flow of up to 0.03 M is studied. The analysis is done experimentally, using the two-microphone three-calibration technique and the results are compared with numerical simulations, using an industrial finite element package. The main application of this study is in the acoustic design of water-cooled charge-air coolers in internal combustion engines. The measurements are done on an effectively semi-infinite narrow pipe. It is shown that neglecting the flow effect in the calibration process of narrow pipes can significantly increase the measurement error. The results show that although the direct modification of the normalized acoustic input impedance due to low Mach number flow is negligible, the flow exerts an indirect but significant effect on this parameter by modifying the thermal gradient profile. Therefore, taking this effect into account can help to achieve an improved acoustical design of engine intake lines.