[en] The heat-transfer behavior of a heat-generating, dry, particulate bed resulting from a postulated core meltdown accident in sodium-cooled fast reactors is investigated theoretically. The processes of combined conduction and thermal radiation in the dry particulate bed and transient heat conduction in the structure in contact with the bed are modeled. Also modeled is the contribution of direct gamma-ray radiation to heat transfer. Results for the transient temperature distribution of the system are obtained by the method of successive approximation. Various post-dryout situations are considered and the conditions leading either to an incipient melting system or to a coolable non-melting system are identified. These are found to depend on four groups of dimensionless parameters, namely, the thermal property group, the radiation and internal heating group, the gamma-ray heating group, and the external cooling group