Measurements of the diagonal magnetothermopower (${\mathit{S}}_{\mathit{xx}}$) of a high-quality two-dimensional hole system reveal that in the diffusion regime (T100 mK), ${\mathit{S}}_{\mathit{xx}}$ at filling factors \ensuremath{\nu}=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 ${\mathit{S}}_{\mathit{xx}}$ at these two fillings can be explained remarkably well based on a recently proposed particle-flux composite-fermion picture.