The present invention provides an extrudable, crosslinked, greasy heat-radiating material which can find completely new ways of use (in terms of methods of operation and putting it in a service area), because it can be formed into any shape after it is extruded from the container in which it is held (e.g., syringe or tube) to be put or placed in a gap of any shape between a heat-generating body and heat-radiating body, where it keeps shape self-retainability even when kept under a very light load, e.g., kept on a slanted plate, unlike the conventional thermoconductive silicone rubber composition or thermoconductive silicone oil compound, whose applicable areas are limited to formed articles, represented by sheet, and coating. The present invention also provides a container filled with and sealing the extrudable, crosslinked, greasy heat-radiating material, process for producing the container, and method of heat radiation using the container. More specifically, the present invention provides the extrudable, crosslinked, greasy heat-radiating material comprising a crosslinked silicone gel (A) dispersed with a thermoconductive filler (B) and shape self-retainable in spite of being fluid, wherein the thermoconductive filler (B) is incorporated at 5 to 500 parts by weight per 100 parts by weight of the crosslinked silicone gel (A); container filled with and sealing the extrudable, crosslinked, greasy heat-radiating material; process for producing the container; and method of heat radiation using the container put or placed in a gap between a heat-generating body and heat-releasing body.