We use a semiclassical three-fluid model to analyse the conditions for spatial phase separation in a mixture of fermionic Li-6 and a (stable) Bose-Einstein condensate of Li-7 atoms under cylindrical harmonic confinement, both at zero and finite temperature. We show that with the parameters of the Paris experiment (Schreck F et al 2001 Phys. Rev. Lett. 87 080403) an increase of the boson-fermion scattering length by a factor five would be sufficient to enter the phase-separated regime. We give examples of configurations for the density profiles in phase separation and estimate that the transition should persist at temperatures typical of current experiments. For higher values of the boson-fermion coupling we also find a new phase separation between the fermions and the bosonic thermal cloud at finite temperature.