The ESR (Electron Spin Resonance) spectrum of the XXZ spin chain with finite length shows a double-peak structure at high temperatures around the EPR (Electron Paramegnetic Resonance) resonance frequency. This fact has been pointed out by direct numerical methods (S. El Shawish, O. Cépas and S. Miyashita: Phys. Rev. B 81, 224421 (2010); H. Ikeuchi, H. De Raedt, S. Bertaina, and S. Miyashita: Phys. Rev. B 92, 214431 (2015)). On the other hand, at low temperatures. the spectrum has a single peak with a finite shift from the frequency of EPR as predicted by the analysis of field theoretical works (M. Oshikawa and I. Affleck: Phys. Rev. Lett. 82, 5136 (1999)). We study how the spectrum changes with the temperature, and also we study the size-dependence of the line shape including the even-odd effect. In order to understand those dependences, we introduce a decomposition of the spectrum into contributions from transitions specified by magnetization, and we characterize the structure of the spectrum by individual contributions. Applying the moment method introduced by M. Brockman et al., to each component, we analyze the size-dependence of the structure of the spectrum, which supports the numerical observation that separation of the double-peak structure vanishes inversely with the size.