A two-fluid time-dependent analytical model of the perturbed solar wind is presented. The expansion of newly emitted material, caused, for instance, by the outburst of a solar flare, is simulated by a spherical piston. The electron collision time is phenomenologically decreased to account for a transit from a collisional (near the sun) to a collisionless regime (at 1 AU). This effectively inhibits thermal conductivity and enhances ion-electron heat exchange. For a given thermal conductivity in the limit of strong coupling, one-fluid flow in a thermally conducting medium is recovered. A pattern of flow which resembles one-fluid in an adiabatic medium may be obtained if heat is removed from the perturbed plasma into the propelling plasma. The perturbed flow consists of a thermal precursor which is followed by a shock across which electrons are isothermal while protons are compressed and heated. For most of the postshock domain the electron temperature is considerably higher than the proton temperature. Finally, we show that the postshock rise and fall of density cannot be used to distinguish piston-driven waves from blast waves.