The specific heat of the one-dimensional anisotropic classical Heisenberg ferromagnet in a magnetic field is calculated by computer simulation. The results are compared with experimental measurements on the linear-chain magnet CsNiF3 and with analytical calculations on the continuum version of the model. Special attention is paid to the dependence of the specific-heat maximum on magnetic field. It is concluded that quantum effects are essential for a proper model of CsNiF3.