Triton's surface shows clear evidences of resurfacing processes such as volcanism, tectonic structures and a very low presence of impact basins, which indicates that Triton's interior could remain active currently. It is generally assumed in icy satellites that the depth of faulting associated with large faults corresponds to the brittle-ductile transition (BDT), and the properties of large faults penetrating to the BDT depth can be used to obtain information on the mechanical behavior of the lithosphere, and potentially can contribute to constrain the thermal state of a planetary body. Here we present a detailed study of Raz Fossae, suggesting that this structure is not only limited to the graben originally described in previous works. Our study shows that north of the classical Raz Fossae there is another trough set with similar structural characteristics that can be interpreted as part of the same system of faults. We have calculated surface heat flows for Triton from the depth of the BDT under both structures: Raz Fossae and the new northern trough set from a detailed analysis of the troughs widths, taking into account the possible composition of the ice shell (H2O and NH3·2H2O). Our results show surface heat flows values much higher than those estimated in previous studies by modeling radiogenic production and tidal dissipation for fixed orbital eccentricities. Furthermore, our results suggest regional differences in the pattern of heat loss throughout Triton's lithosphere.