  In this paper we obtain holographic formulas for the transport coefficients
$\kappa$ and $\tau_\pi$ present in the second-order derivative expansion of
relativistic hydrodynamics in curved spacetime associated with a non-conformal
strongly coupled plasma described holographically by an Einstein+Scalar action
in the bulk. We compute these coefficients as functions of the temperature in a
bottom-up non-conformal model that is tuned to reproduce lattice QCD
thermodynamics at zero baryon chemical potential. We directly compute, besides
the speed of sound, 6 other transport coefficients that appear at second-order
in the derivative expansion. We also give an estimate for the temperature
dependence of 11 other transport coefficients taking into account the simplest
contribution from non-conformal effects that appear near the QCD crossover
phase transition. Using these results, we construct an Israel-Stewart-like
theory in flat spacetime containing 13 of these 17 transport coefficients that
should be suitable for phenomenological applications in the context of
numerical hydrodynamic simulations of the strongly-coupled, non-conformal
quark-gluon plasma. Using several different approximations, we give
parametrizations for the temperature dependence of all the second-order
transport coefficients that appear in this theory in a format that can be
easily implemented in existing numerical hydrodynamic codes.
