Direct numerical simulations of an Eulerian-based carrier phase are performed which are two-way coupled in momentum and energy to Lagrangian droplets within a Boussinesq-type incompressible formulation, where the droplets are allowed to evaporate and condense and are thus coupled to the vapor field of the carrier phase. Turbulent planar Couette flow is simulated under varying boundary forcings to understand the degree to which evaporating droplets modify vertical fluxes of energy in horizontally homogeneous systems. In particular, the separate influences on both sensible and latent heat are substantial but opposite in sign, and the local relative humidity can result in droplet-induced heat or moisture fluxes which counteract the prescribed background gradients. The influence of droplet Stokes number is also considered, where it is shown that both clustering and turbophoresis play important roles in determining the magnitude of the droplet-induced sensible and latent heat fluxes.