For all transport processes other than heat transfer, the shared field is the same as the transported quantity in the equation. However, in the case of heat transfer, it is temperature that is shared but enthalpy that is transported. Hence, CFX does not solve a bulk enthalpy equation, but rather solves a separate enthalpy equation for each fluid with a large interphase heat transfer term, which forces the temperature fields to be the same.
The equations solved are identical to the phasic equations for full multiphase described above. For homogeneous heat transfer model, the interphase heat transfer coefficient is not modeled by any of the correlations used in full multiphase. Instead it is chosen to be large relative to the other transported processes in the equation, thereby ensuring the phasic temperatures are the same.