  The double-layer Heisenberg antiferromagnet with intra- and inter-layer
couplings $J$ and $J_\perp$ exhibits a zero temperature quantum phase
transition between a quantum disordered dimer phase for $g>g_c$ and a Neel
phase with long range antiferromagnetic order for $g<g_c$, where $g=J_\perp/J$
and $g_c \approx 2.5$. We consider the behavior of the system at finite
temperature for $g \ge g_c$ using two different and complementary approaches;
an analytical Brueckner approximation and numerically exact quantum Monte Carlo
simulations. We calculate the temperature dependent spin excitation spectrum
(including the triplet gap), dynamic and static structure factors, the specific
heat, and the uniform magnetic susceptibility. The agreement between the
analytical and numerical approaches is excellent. For $T \to 0$ and $g \to
g_c$, our analytical results for the specific heat and the magnetic
susceptibility coincide with those previously obtained within the nonlinear
$\sigma$ model approach for $N\to \infty$. Our quantum Monte Carlo simulations
extend to significantly lower temperatures than previously, allowing us to
obtain accurate results for the asymptotic quantum critical behavior. We also
obtain an improved estimate for the critical coupling: $g_c = 2.525 \pm 0.002$.
