We analyze the temperature dependence of the electron spin resonance linewidth above the critical region in exchange-coupled magnetic insulators. The focus is on separating the contributions to the linewidth from spin-spin interactions, spin-one-phonon interactions and spin-two-phonon interactions at temperatures where the spin-spin term is constant and the one- and two-phonon terms vary as T and T^2, respectively. Taking Co3O4 as an example, we use a least squares fit over the temperature range 50 K < T < 500 K to obtain values of the three components. It is found that the spin-spin mechanism is dominant below 100 K, while the two-phonon mechanism is most important above 250 K. In the intermediate region, all three mechanisms make significant contributions.