Measurements of the diagonal magnetothermopower (S-xx) of a high-quality two-dimensional hole system reveal that the diffusion regime (T < 100 mK), S-xx at filling factors v = 1/2 and 3/2 depends approximately linearly on temperature and has a much smaller magnitude than expected for noninteracting particles at half-filled Landau levels. We show that both the temperature dependence and the magnitude of S-xx at these two fillings can be explained remarkably well based on a recently proposed particle-flux composite-fermion picture.