This paper presents innovative iteration algorithms for multi-interface heat transfer in pipe flow. To the best of our knowledge, this is the first approach derived from the drift-flux model (DFM), which is more competent than mechanistic models for high-slippage gas/liquid flow. The mass-and momentum-conservation equations are inherited from literature and we have written them in the differential forms. In parallel, we thoroughly analyzed the heat-flux conservation among different layers and successfully presented the derivatives of temperature in location and time. Finally, the solution is obtained numerically to capture the temperature/pressure-distribution profiles under transient conditions. For waxy-crude fields, it is critical to sustain the flowing temperature above the wax-appearance temperature. This is especially challenging for gas-lift-assisted wells. The injected gas, commonly at a relatively low temperature, makes this flow-assurance problem sophisticated. An effective practice is to heat up the flowing fluid by installing an electrical cable in tubing. The heat exchange happens at three interfaces in the production system: between cable and flowing crude, flowing crude and injected gas, and injected gas and formation. It is challenging to model such a multiphase production system, including an inner annulus inside the tubing, because once the electrical cable is installed, an outer annulus is where the gas is injected. To optimize this production system, a rigorous transient multiphase and multi-interface heat-transfer simulator is required. By integrating the subsurface boundary condition explicitly, new algorithms can optimize the cable length, heating period, supplied power, or gas-injection rate for the aforementioned production system. This new method has been applied successfully for several gas-lift-assisted wells in a waxy-crude field located in northern China. The power consumption has decreased noticeably by 30% more than the historical field performance. The delegated optimization scheme reduces the shut-in time in winters, which promises cost-savings. The presented model not only satisfies the exceptional modelling requirements for periodically heating crude producers, but it also is appropriate for other heat-transfer investigations under transient multi-interface and multiphase-flow conditions.