Electronically conducting polymers constitute an emerging class of materials for novel electronics, such as printed electronics and flexible electronics. Their properties have been further diversified to introduce elasticity, which has opened new possibility for "stretchable" electronics. Recent discoveries demonstrate that conducting polymers have thermoelectric properties with a low thermal conductivity, as well as tunable Seebeck coefficients - which is achieved by modulating their electrical conductivity via simple redox reactions. Using these thermoelectric properties, all-organic flexible thermoelectric devices, such as temperature sensors, heat flux sensors, and thermoelectric generators, are being developed. In this article we discuss the combination of the two emerging fields: stretchable electronics and polymer thermoelectrics. The combination of elastic and thermoelectric properties seems to be unique for conducting polymers, and difficult to achieve with inorganic thermoelectric materials. We introduce the basic concepts, and state of the art knowledge, about the thermoelectric properties of conducting polymers, and illustrate the use of elastic thermoelectric conducting polymer aerogels that could be employed as temperature and pressure sensors in an electronic-skin.