Using the Hamiltonian formulation for composite fermions developed recently, the temperature dependence of the spin polarization is computed for the translationally invariant fractional quantum Hall states at ν = 1/3 and ν = 2/5 in two steps. In the first step, the effect of particle-hole excitations on the spin polarization is computed in a composite-fermion Hartree-Fock approximation. The computed magnetization for ν = 1/3 lies above the experimental results for intermediate temperatures indicating the importance of long-wavelength spin fluctuations which are not correctly treated in the Hartree-Fock approximation. In the second step, spin fluctuations beyond the Hartree-Fock approximation are included for ν = 1/3 by mapping the problem onto the coarse-grained continuum quantum ferromagnet. The parameters of the description in terms of the effective continuum quantum ferromagnet are extracted from the preceding Hartree-Fock analysis. After the inclusion of spin fluctuations in a large-N approach, the results for the finite-temperature spin polarization are in quite good agreement with the experiments.