A computer system includes a rack-mountable server unit with a closed server housing. The server housing has a channel with a recessed channel wall in conductive thermal communication with a processor or other heat-generating component. An elongate conduit is received into the channel of the server housing in conductive thermal communication with an external surface of the server housing. The server is cooled by conductive fluid flow through the conduit, with no appreciable airflow through the server housing. The system may be operated in an optional burst cooling mode, wherein a volume of cooling fluid is trapped in the conduit for a period of time before being quickly released.