  The quark gluon plasma produced in heavy ion collisions behaves like an
almost ideal fluid described by viscous hydrodynamics with a number of
transport coefficients. The second order coefficient $\kappa$ is related to a
Euclidean correlator of the energy-momentum tensor at vanishing frequency and
low momentum. This allows for a lattice determination without maximum entropy
methods or modelling, but the required lattice sizes represent a formidable
challenge. We calculate $\kappa$ in leading order lattice perturbation theory
and simulations on $120^3\times 6,8$ lattices with $a<0.1$ fm. In the
temperature range $2T_\mathrm{c}-10T_\mathrm{c}$ we find $\kappa=0.36(15)T^2$.
The error covers both a suitably rescaled AdS/CFT prediction as well as,
remarkably, the result of leading order perturbation theory. This suggests that
appropriate noise reduction methods on the lattice and NLO perturbative
calculations could provide an accurate QCD prediction in the near future.
