The temperature evolution in and around a heated infinite cylinder with tubular sheath is studied, allowing for surface resistances between the cylindrical core and sheath, as well as between the sheath and surrounding medium. This configuration was initially investigated in the framework of the thermal conductivity measurements made by the Apollo 15 and 17 missions to the Moon. Only the equilibration case was used in this context. We derive corresponding equations for arbitrary active heating of the cylinder core and sheath. Typical applications are the determination of the temperature increase and the heat loss of buried cables, and the temperature evolution in thermal conductivity sensors. An example of the latter is used to illustrate some consequences of low surface conductances. (C) 2012 Elsevier Ltd. All rights reserved.