We present here a fully coupled flux-based electro-thermal simulation package. We simulate the electrical characteristics using a full-band Cellular Monte Carlo approach (CMC), which calculates the heat generation rate within each computational cell directly from the energy exchanged through electron-phonon scattering events. We then use this calculated generation rate in a flux-based thermal solver producing physically realistic temperature maps for both optical and acoustic modes by solving a Poisson-like equation for each respectively. The resulting temperature map is then used to update scattering rates reflecting the local temperature in each individual cell. In addition, temperature-dependent thermal conductivities are included using the Kirchhoff Transformation, which implicitly includes the temperature dependence in a new apparent temperature variable while allowing us to solve a Poisson-like linear elliptical partial differential equation.