  We investigate the applicability of finite temperature random phase
approximation (RPA) using a solvable Lipkin model. We show that the finite
temperature RPA reproduces reasonably well the temperature dependence of total
strength, both for the positive energy (i.e., the excitation) and the negative
energy (i.e., the de-excitation) parts. This is the case even at very low
temperatures, which may be relevant to astrophysical purposes.
