  Within the relativistic mean-field framework with hadron masses and coupling
constants dependent on the mean scalar field we study properties of nuclear
matter at finite temperatures, baryon densities and isospin asymmetries
relevant for heavy-ion collisions at laboratory energies below 2$A$ GeV.
Previously constructed (KVORcut-based and MKVOR-based) models for the
description of the cold hadron matter, which differ mainly by the density
dependence of the nucleon effective mass and symmetry energy, are extended for
finite temperatures. The baryon equation of state, which includes nucleons and
$\Delta$ resonances is supplemented by the contribution of the pion gas
described either by the vacuum dispersion relation or with taking into account
the $s$-wave pion-baryon interaction. Distribution of the charge between
components is found. Thermodynamical characteristics on $T-n$ plane are
considered. The energy-density and entropy-density isotherms are constructed
and a dynamical trajectory of the hadron system formed in heavy-ion collisions
is described. The effects of taking into account the $\Delta$ isobars and the
$s$-wave pion-nucleon interaction on pion differential cross sections, pion to
proton and $\pi^-/\pi^+$ ratios are studied. The liquid-gas first-order phase
transition is studied within the same models in isospin-symmetric and
asymmetric systems. We demonstrate that our models yield thermodynamic
characteristics of the phase transition compatible with available experimental
results. In addition, we discuss the scaled variance of baryon and electric
charge in the phase transition region. Effect of the non-zero surface tension
on spatial redistribution of the electric charge is considered for a possible
application to heavy-ion collisions at low energies.
