We report neutron diffraction and magnetization studies of the magnetic order in multiferroic BiFeO3. In ferroelectric monodomain single crystals, there are three magnetic cycloidal domains with propagation vectors equivalent by crystallographic symmetry. The cycloid period slowly grows with increasing temperature. The magnetic domain populations do not change with temperature except in the close vicinity of the Neel temperature, at which, in addition, a small jump in magnetization is observed. No evidence for the spin-reorientation transitions proposed in previous Raman and dielectric studies is found. The magnetic cycloid is slightly anharmonic for T = 5 K. The anharmonicity is much smaller than previously reported in nuclear magnetic resonance studies. At room temperature, a circular cycloid is observed, within errors. We argue that the observed anharmonicity provides important clues for understanding electromagnons in BiFeO3.