This manuscript proposes a time-series temperature-dependent power flow method for unbalanced distribution networks consisting of underground cables. A thermal circuit model for unbalanced three-phase multi-core cables is developed to estimate the conductor temperature and resistance of Medium and Low Voltage distribution networks. More specifically, a novel approach is proposed to model and estimate the parameters of the three-phase thermal circuit of 3/4-core cables, using the results of Finite Element Method and Particle Swarm Optimization. The proposed approach is generic and can be accurately applied to any kind of 3- or 4-core cables buried in homogeneous or non-homogeneous soil. Furthermore, it is applicable in cases where one or more adjacent cables exist. Using the proposed approach, the conductor temperature of each phase can be individually and precisely calculated even in networks with highly unbalanced loads. The proposed approach is expected to be an important tool for simulating the steady state of unbalanced distribution networks and estimating the conductor temperatures. The proposed thermal circuit is validated using two 4-core LV and one 3-core MV cables buried in different depths in homogeneous or non-homogeneous soil. Time-series power flow for a whole year is performed in a 25-bus unbalanced LV network consisting of multicore underground cables.