  We calculate Curie temperatures and study the stability of ferromagnetism in
diluted magnetic materials, taking as a model for the exchange between magnetic
impurities a damped Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and a shor
t range term representing the effects of superexchange. To properly include
effects of spin and thermal fluctuations as well as geometric disorder, we
solve the effective Heisenberg Hamiltonian by means of a recently developed
semi-analytical approach. This approach, ``self-consistent local Random Phase
Approximation (SC-L RPA)'', is explained. We show that previous mean-field
treatments, which have been widely used in the literature, largely overestimate
both the Curie temperatures and the stability of ferromagnetism as a function
of carrier density. The discr epancy when compared to the current approach was
that effects of frustration in RKKY oscillations had been strongly
underestimated by such simple mea n-field theories. We argue that the use, as
is frequent, of a weakly-disordered RKKY exchange to model ferromagnetism in
diluted III-V systems is inconsistent with the observation of ferromagnetism
over a wide region of itinerant carrier densities. This may be puzzling when
compared to the apparent success of calculations based on {\it ab-initio}
estimates of the coupling; we propose a resolution to this issue by taking
RKKY-like interactions between resonant states close to the Fermi level.
