Employing Zeldovich's (1940) quasi-one-dimensional formulation the multiplicity of detonation regimes occasionally observed in obstacle-laden systems is explored. The paper is an extension of the previously studied adiabatic version of the problem where, in addition to the well-known sub-CJ quasi-detonation, the low-speed supersonic as well as subsonic detonation regimes were identified. It is shown that the hysteresic loop associated with non-uniqueness of detonation regimes may be located entirely within the supersonic domain, the situation often encountered in experiments. By adopting a one-step bimolecular kinetics the well known dependency of the transition on the initial pressure is explained. The incorporation of heat losses, apart from bringing up detonability limits, strongly affects the low-speed regimes. The latter are found to occur only in the systems where the Reynolds analogy is strongly violated (rough tubes, porous media), and do not arise in smooth-walled tubes. The disparity between detonability and flammability limits is discussed.