When an ordered spin system of a given dimensionality undergoes a second order phase transition, the dependence of the order parameter, i.e., magnetization on temperature, can be well described by thermal excitations of elementary collective spin excitations (magnons). However, the behavior of magnons themselves, as a function of temperature and across the transition temperature T_C, is an unknown issue. Utilizing spin-polarized high resolution electron energy loss spectroscopy, we monitor the high-energy (terahertz) magnons, excited in an ultrathin ferromagnet, as a function of temperature. We show that the magnonsénergy and lifetime decrease with temperature. The temperature-induced renormalization of the magnonsénergy and lifetime depends on the wave vector. We provide quantitative results on the temperature-induced damping and discuss the possible mechanism, e.g., multimagnon scattering. A careful investigation of physical quantities determining the magnons\'propagation indicates that terahertz magnons sustain their propagating character even at temperatures far above T_C.