The heat flow during circumferential welding of a small-diameter aluminium pipe, which cannot be assumed to be in the quasi-stationary state because of heat accumulation, was analysed by employing a semi-analytical finite element method. The circumferential distribution of arc heat flux and temperature was simulated in the form of an expanded series to calculate the three-dimensional heat flow with a two-dimensional solution domain. The arc heat distribution, assumed as a Gaussian form, was expressed in several circumferential line heat sources by using the Fourier series expansion. The solution domain was divided into two sub-domains to apply the two types of series with two different numbers of the expanding term, which results in the reduction of the calculation time. The thermal cycles and isotherms in the rz plane calculated by using the proposed semi-analytical finite element method agreed fairly well with the experimental results adopted from a reference. Due to the heat buildup the fusion zone increases in its size as the welding proceeds. The temperature near the heat source rises also as the welding proceeds, but the shape of the circumferential temperature distribution of a ring element was maintained almost unchanged during the entire welding process except the welding start. The proposed semi-analytical finite element method could be considered as very useful for analysing the heat flow in circumferential welding of small-diameter pipes because of its simple formulation and short computing time.