Recent observations show cool, oscillating prominence threads fading when observed in cool spectral lines and appearing in warm spectral lines. A proposed mechanism to explain the observed temperature evolution is that the threads were heated by turbulence driven by the Kelvin-Helmholtz instability that developed as a result of wave-driven shear flows on the surface of the thread. As the Kelvin-Helmholtz instability is an instability that works to mix the two fluids on either side of the velocity shear layer, in the solar corona it can be expected to work by mixing the cool prominence material with that of the hot corona to form a warm boundary layer. In this paper, we develop a simple phenomenological model of nonlinear Kelvin-Helmholtz mixing, using it to determine the characteristic density and temperature of the mixing layer. For the case under study, with constant pressure across the two fluids, these quantities are {ρ }mixed}=\sqrt{{ρ }1{ρ }2} and {T}mixed}=\sqrt{{T}1{T}2}. One result from the model is that it provides an accurate—as determined by comparison with simulation results—determination of the kinetic energy in the mean velocity field. A consequence of this is that the magnitude of turbulence—and with it, the energy that can be dissipated on fast timescales—as driven by this instability can be determined. For the prominence-corona system, the mean temperature rise possible from turbulent heating is estimated to be less than 1% of the characteristic temperature (which is found to be T mixed = 105 K). These results highlight that mixing, and not heating, is likely to be the cause of the observed transition between cool to warm material. One consequence of this result is that the mixing creates a region with higher radiative loss rates on average than either of the original fluids, meaning that this instability could contribute a net loss of thermal energy from the corona, i.e., coronal cooling.