  The back-reaction of the perturbed thermal equilibrium in the solar corona on
compressive perturbations, also known as the effect of wave-induced thermal
misbalance, is known to result in thermal instabilities chiefly responsible for
the formation of fine thermal structuring of the corona. We study the role of
the magnetic field and field-aligned thermal conduction in triggering
instabilities of slow magnetoacoustic and entropy waves in quiescent and hot
active region loops, caused by thermal misbalance. Effects of the magnetic
field are accounted for by including it in the parametrisation of a guessed
coronal heating function, and the finite plasma parameter $\beta$, in terms of
the first-order thin flux tube approximation. Thermal conduction tends to
stabilise both slow and entropy modes, broadening the interval of plausible
coronal heating functions allowing for the existence of a thermodynamically
stable corona. This effect is most pronounced for hot loops. In contrast to
entropy waves, the stability of which is found to be insensitive to the
possible dependence of the coronal heating function on the magnetic field, slow
waves remain stable only for certain functional forms of this dependence,
opening up perspectives for its seismological diagnostics in future.
