To date, the vast majority of kinetic-theory-based models for rapid granular flows have been based on a Navier-Stokes-level approximation. In particular, a perturbative Chapman-Enskog expansion has been carried out to first order about low Knudsen number (i.e., small spatial gradients in the hydrodynamic variables). As part of the current effort, the validity of this approximation is rigorously checked for each of the constitutive relations – stress, heat flux, and dissipation rate. To accomplish this task, hard-sphere molecular dynamics (MD) simulations are employed for a system characterized by a granular temperature gradient and zero mean flow. The resulting hydrodynamic profiles are used as inputs to the kinetic-theory expressions, in order to preclude a propagation of error arising from the solution of the corresponding boundary value problem. These constitutive quantities are then compared to those extracted directly from MD. The results indicate that higher-order effects are present for each of the three constitutive quantities. Of particular importance is the role of higher-order effects in the heat flux; these effects account for a correction, based on percentage of Navier-Stokes-order values, that is about one order of magnitude greater than those associated with stress or dissipation rate. Furthermore, because symmetry considerations indicate that no second-order (Burnett order) contributions are non-existent for heat flux, the higher-order contributions are attributed to third-order gradients (super Burnett order) or higher.