  We study a model of a composite system constructed from a "pairing layer" of
disconnected attractive-U Hubbard sites that is coupled by single-particle
tunneling, t_perp, to a disordered metallic layer. For small inter-layer
tunneling the system is described by an effective long-range XY phase model
whose critical temperature, T_c, is essentially insensitive to the disorder and
is exponentially suppressed by quantum fluctuations. T_c reaches a maximum for
intermediate values of t_perp, which we calculate using a combination of
mean-field, classical and quantum Monte Carlo methods. The maximal T_c scales
as a fraction of the zero temperature gap of the attractive sites when U is
smaller than the metallic bandwidth, and is bounded by the maximal T_c of the
two-dimensional attractive Hubbard model for large U. Our results indicate that
a thin, rather than a thick, metallic coating is better suited for the
enhancement of T_c at the surface of a phase fluctuating superconductor.
