[en] Phase co-existence and heat transport in two dimensional systems are of always under active research in various disciplines of physics. We report an experimental observation of liquid–crystal phase co-existence in Dusty Plasma Experimental (DPEx) device. The dusty plasma system is found to be in crystal state at high neutral gas pressure and in liquid state when the pressure is reduced to a critical value. Interestingly, phase co-existence is observed in the inter-mediate pressure range in which a hot liquid state (temperature 2.5 eV) is surrounded by a cold crystal structure (0.1 eV). Crystal and liquid states are analysed through a host of structural analysis like pair correlation function, Voronoi diagram, Delaunay diagram and orientational order parameter estimation, whereas the screened Coulomb coupling parameter and dust temperature are estimated using Langevin dynamics. The heat transport length is then deduced from the temperature profile to estimate the thermal diffusivity and conductivity. This technique allows a non-invasive method to estimate the heat transport parameters unlike the experiments carried out in past. The present set of measurements shows a strong thermal gradient in the system and the estimated heat transport length is found to be less than the measurements carried out in other complex plasma experiments. Presence of few particles beneath the crystal structure is found as the possible reason of the phase co-existence which heatup the dust particles on the top by the non-reciprocal force arising from the ion wake formation mechanism. (author)