A new reduced-order model accounting for a thermal damping effect on a radial motion of a spherical bubble is proposed. The present model is based on that developed by Preston et al. (2002). A temperature gradient at the bubble wall is approximated by use of an average bubble temperature and a thermal penetration length inside the bubble based on a linear theory (Prosperetti, 1991). A phase difference between the temperature gradient and the average temperature is taken into account. In the present report, a perturbation analysis of the bubble motion is performed. The result of the present model shows good agreement with the second order theory (Sugiyama et al., 2004), in which the temperature distribution inside the bubble is fully considered. The reason for the agreement is discussed.