  We study scaling behavior in 2D, S=1/2 and S=1 Heisenberg antiferromagnets
using the data on full q-dependences of the equal time structure factor and the
static susceptibility, calculated through high temperature expansions. We also
carry out comparisons with a model of two coupled S=1/2 planes with the
interlayer coupling tuned to the T=0 critical point. We separately determine
the spin-wave velocity c and mass $m=c/\xi$, in addition to the correlation
length, $\xi$, and find that c is temperature dependent; only for $T\alt JS$,
it approaches its known T=0 value $c_0$. Despite this temperature dependent
spin-wave velocity, full q- and $\omega$-dependences of the dynamical
susceptibility $\chi(\bf q,\omega)$ agree with the universal scaling functions
computable for the $\sigma$-model, for temperatures upto $T_0 \sim 0.6c_0/a$.
Detailed comparisons show that below $T_0$ the S=1 model is in the renormalized
classical (RC) regime, the two plane model is in the quantum critical (QC)
regime, and the S=1/2 model exhibits a RC-QC crossover, centered at T=0.55J. In
particular, for the S=1/2 model above this crossover and for the two-plane
model at all T, the spin-wave mass is in excellent agreement with the universal
QC prediction, $m\simeq 1.04\,T$. In contrast, for the S=1/2 model below the
RC-QC crossover, and for the S=1 model at all T, the behavior agrees with the
known RC expression. For all models nonuniversal behavior occurs above $T\sim
0.6c_0/a$. Our results strongly support the conjecture of Chubukov and Sachdev
that the S=1/2 model is close to the T=0 critical point to exhibit QC behavior.
