  We present an accurate and efficient real-space formulation of the
Hellmann-Feynman stress tensor for $\mathcal{O}(N)$ Kohn-Sham density
functional theory (DFT). While applicable at any temperature, the formulation
is most efficient at high temperature where the Fermi-Dirac distribution
becomes smoother and density matrix becomes correspondingly more localized. We
first rewrite the orbital-dependent stress tensor for real-space DFT in terms
of the density matrix, thereby making it amenable to $\mathcal{O}(N)$ methods.
We then describe its evaluation within the $\mathcal{O}(N)$ infinite-cell
Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable
to metallic as well as insulating systems, is highly parallelizable, becomes
increasingly efficient with increasing temperature, and provides results
corresponding to the infinite crystal without the need of Brillouin zone
integration. We demonstrate systematic convergence of the resulting formulation
with respect to SQ parameters to exact diagonalization results, and show
convergence with respect to mesh size to established planewave results. We
employ the new formulation to compute the viscosity of hydrogen at a million
kelvin from Kohn-Sham quantum molecular dynamics, where we find agreement with
previous more approximate orbital-free density functional methods.
