The classic theory of buoyant motion of a free planar heated jet in still air is extended to account for environmental winds from the same direction as the jet, that is, co-flowing winds. The model is applicable for wind and jet velocities up to 100 m/sec, and jet temperatures up to three times the ambient. Calculations are made for initial jet velocities of 5 and 20 m/sec and temperature excesses, relative to ambient temperature, of 0.3 and 1. For light winds relative to the initial jet velocity the vertical velocity and centerline trajectory of the plume rise rapidly with distance from the jet source. This is similar to that found with the classic theory for still air. As the wind speed approaches the initial jet velocity, the rise of the jet plume with distance from the source is much more gradual. For all wind speeds, the axial jet velocity and temperature decrease rapidly with distance from the jet source, until they become almost constant at short distances downstream. A similarity rule is derived which preserves dynamic similarity in scaling from a given system to another system. For low wind speeds the procedure is close to that based on constant Froude number. (Author).