The line-width of carbon nanotubes (CNTs) was studied as a function of the temperature at a frequency of 9.49 GHz in the presence of external electromagnetic radiation. The relative frequency dependence of the absorption power is obtained with the projection operator technique (POT) proposed by Kawabata. The line-width increased as the temperature increased in the high-temperature region (T>200 K). The scattering is little affected in the low-temperature region (T<200 K) because there is no correlation between the resonance field and the Fermi-Dirac distribution function. Thus, the present technique is considered to be more convenient to explain the resonant system as in the case of other optical transition problems.