This work deals with the thermal-hydraulics of a melt pool coupled with the physical chemistry for thepurpose of describing the behaviour of mixtures of materials (non-eutectic).Evolution of transient temperature in a liquid melt pool heated by volumetric power dissipation hasbeen described with solidification on the cooled wall. The model has been developed and is validatedfor the experimental results given by LIVE experiment, performed at Karlsruhe Institute ofTechnology (KIT) in Germany. Under the conditions of these tests, it is shown that the interfacetemperature follows the liquidus temperature (corresponding to the composition of the liquid bath)during the whole transient. Assumption of interface temperature as liquidus temperature allowsrecalculating the evolution of the maximum melt temperature as well as the local crust thickness.Furthermore, we propose a model for describing the interaction between a non-eutectic liquid meltpool (subjected to volumetric power dissipation) and an ablated wall whose melting point is below theliquidus temperature of the melt. The model predictions are compared with results of ARTEMIS 2Dtests. A new formulation of the interface temperature between the liquid melt and the solid wall(below liquidus temperature) has been proposed.