We consider the problem of obtaining maximum work from an arbitrary two degree of freedom working fluid coupled to a periodic source of pumped thermal energyf (t). The working fluid is also coupled to a heat bath of temperatureTex(t) by a conductor of conductanceK. We assume thatf (t) andTex(t) are given functions of time which are piecewise continuous but are otherwise arbitrary. For periodicf (t) andTex(t) we find that the available power is given by the variance off+KTexover the period. Even withf0, the result is interesting. It reduces to the Curzon–Ahlborn7power for step functionTex(t). It also provides a measure of the power available from temperature fluctuations of the atmosphere.