The equation of state (EoS) and composition of dense and hot ∆-resonance admixed hypernuclear matter is studied under conditions that are characteristic of neutron star binary merger remnants and supernovas. The cold, neutrino free regime is also considered as a reference for the astrophysical constraints on the EoS of dense matter. Our formalism uses the covariant density functional (CDF) theory successfully adapted to include the full J P = 1/2 + baryon octet and non-strange members of J P = 3/2 + decouplet with density-dependent couplings that have been suitably adjusted to the existing laboratory and astrophysical data in the nuclear and hypernuclear sectors. The effect of ∆-resonances at finite temperatures is to soften the EoS of hypernuclear matter at intermediate densities and stiffen it at high densities. At low temperatures, the heavy baryons Λ, ∆ − ,Ξ − , Ξ 0 and ∆ 0 appear in the given order if the ∆-meson couplings are close to those for the nucleon-meson couplings. As is the case for hyperons, the thresholds of ∆-resonances move to lower densities with the increase of temperature indicating a significant fraction of ∆s in the low-density subnuclear regime. We find that the ∆-resonances comprise a significant fraction of baryonic matter, of the order of 10% at temperatures of the order of several tens of MeV in the neutrino-trapped regime and, thus, may affect the supernova and binary neutron star dynamics.PACS. 9 7.60.Jd (Neutron stars) -2 6.60.+c (Nuclear matter aspects of neutron stars) -2 1.65.+f (Nuclear matter)