  Slow magnetoacoustic waves represent an important tool for probing the solar
coronal plasma. We quantitatively assess the applicability of the weak thermal
conduction theory to coronal seismology by slow waves. We numerically model the
linear standing slow wave in a 1D coronal loop, with field-aligned thermal
conduction $\kappa_\parallel$ as a free parameter and no restrictions on its
efficiency. The time variations of the perturbed plasma parameters, obtained
numerically with full conductivity, are treated as potential observables and
analysed with the standard data processing techniques. The slow wave
oscillation period is found to increase with $\kappa_\parallel$ by about 30%,
indicating the corresponding modification in the effective wave speed, which is
missing from the weak conduction theory. Phase shifts between plasma
temperature and density perturbations are found to be well consistent with the
approximate weakly conductive solution for all considered values of
$\kappa_\parallel$. In contrast, the comparison of the numerically obtained
ratio of temperature and density perturbation amplitudes with the weak theory
revealed relative errors up to 30-40%. We use these parameters to measure the
effective adiabatic index of the coronal plasma directly as the ratio of the
effective slow wave speed to the standard sound speed and in the polytropic
assumption, which is found to be justified in a weakly conductive regime only,
with relative errors up to 14% otherwise. The damping of the initial
perturbation is found to be of a non-exponential form during the first cycle of
oscillation, which could be considered as an indirect signature of entropy
waves in the corona, also not described by weak conduction theory. The
performed analysis and obtained results offer a more robust scheme of coronal
seismology by slow waves, with reasonable simplifications and without the loss
of accuracy.
