At present, two theoretical analysis methods, nonlinear coupled-mode theory and nonlinear Lugiato-Lefever equation (LLE) model, are used to investigate the generation of Kerr optical frequency comb in micro-ring resonators. In previous theoretical studies, only dispersion and optical nonlinear effects were generally considered, and the thermal effects in micro-ring resonators under strong pumping were ignored. In this paper, in view of the thermal effect in the micro-ring resonator induced by the traveling light beam, the nonlinear LLE is modified, and based on the modified equation, the generation of Kerr optical frequency comb is investigated for the two cases of fixing and adjusting the initial detuning. Generation mechanisms of the Kerr optical frequency comb based on these two different ways are analyzed. The characteristics of the Kerr optical frequency comb generated by the two ways are compared, and the reason that causes their difference is investigated.