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Abstract. The energy balance of the analytical solutions of for a steady state of an externally heated/cooled 2-D circumstellar envelope is investigated. It is found that the required heating/cooling rates are physically realistic and can be related to specific microscopic mechanisms. We find that in the subsonic region of the wind the fluid is mechanically heated. In the supersonic stellar envelope the fluid is cooled at a rate which is consistent with radiative cooling to space. The energy balance of steady shell or blob formation in the envelopes of luminous early or late type supergiants is also investigated (Kakouris & Moussas 1998). We find that radiative cooling occurs in the intermediate deceleration region of the three-zone envelope. Indicative of the local thermodynamic processes is the effective polytropic index α which takes values close to the star between 1 and 4, becoming 2 at larger distances. The heated subsonic region close to the stellar surface is isothermal and becomes adiabatic at the sonic transition. We find that the polytropic index α is less than unity in the vicinity of the dense blob, indicating that the region may be dominated by convection.