  Aims: We investigate the thermal and chemical structure in the near-core
region of stars with a convective core by means of gravito-inertial modes. We
do so by determining the probing power of different asteroseismic observables
and fitting methodologies. We focus on the case of the B-type star
KIC$\,$7760680, rotating at a quarter of its critical rotation velocity.
Methods: We compute grids of 1D stellar structure and evolution models for two
different prescriptions of the temperature gradient and mixing profile in the
near-core region. We determine which of these prescriptions is preferred
according to the prograde dipole modes detected in 4-yr $\textit{Kepler}$
photometry of KIC$\,$7760680. We consider different sets of asteroseismic
observables and compare the outcomes of the regression problem for a $\chi^2$
and Mahalanobis Distance merit function, where the latter takes into account
realistic uncertainties for the theoretical predictions and the former does
not. Results: Period spacings of modes with consecutive radial order offer a
better diagnostic than mode periods or mode frequencies for asteroseismic
modelling of stars revealing only high-order gravito-inertial modes. We find
KIC$\,$7760680 to reveal a radiative temperature gradient in models with
convective boundary mixing, but less complex models without such mixing are
statistically preferred for this rotating star, revealing extremely low
vertical envelope mixing. Conclusions: Our results strongly suggest the use of
measured individual period spacing values for modes of consecutive radial order
as an asteroseismic diagnostic for stellar modelling of B-type pulsators with
gravito-inertial modes.
