We apply the Schwinger boson mean-field theory to the square-lattice Heisenberg antiferromagnet at low temperatures. For spin \textonehalf{} we confirm the renormalized classical behavior of the correlation length ${\ensuremath{\kappa}}^{\ensuremath{-}1}(T)$ without appealing to spin-wave theory. We also present a detailed calculation of the dynamical structure factor. A quasielastic peak is featured near $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$, while for $|\mathbf{q}\ensuremath{-}(\ensuremath{\pi},\ensuremath{\pi})|\ensuremath{\gg}\ensuremath{\kappa}$, spin-wave ridges appear. The uniform susceptibility interpolates between spin-wave results at $T=0$ and the high-temperature series of Rushbrooke and Wood. Our theory is distinct from theories in which fermionic spinon excitations determine the low-temperature spin dynamics.