  We investigate the fluctuation contribution to the specific heat of a
two-dimensional superconductor with a non-Fermi normal state described by a
Anderson Green's function
$G(k,i\omega)=\omega_c^{-\alpha}/(i\omega-\epsilon_k)^{1-\alpha}$. The specific
heat corrections contain a term proportional to
$(T^{2\alpha-T_c^{2\alpha}})^{-1}$ and another logarithmic one. We defined a
coherence length as function of the non-Fermi parameter $\alpha$, which showed
that a crossover study between BCS and Bose-Einstein condensation is possible
by varying $\alpha$ in an interval $0 \div \alpha_{cr}$. By comparing our
theoretical results with the experimental data for HTSC materials, we
reobtained the value for $\alpha$, corresponding to such systems, of the order
$0.3 \div 0.45$. We also reobtained the critical temperature for such a
superconductor using the Thouless criterion.
