In this work, we analyze the thermocapillary-enhanced melting of n-octadecane driven by a constant heat flux, applied at the free surface, in microgravity. The material is enclosed in an open rectangular container of dimensions 2L x H, and its solid-to-liquid transition is described using an enthalpy-porosity formulation of the Navier-Stokes equations, assuming laminar and incompressible flow. We study the influence of key governing parameters, including the effect of the heated length Ĩphi is an element of (0, 1], the applied flux phi ⢚ is an element of (0, 8], and the container aspect ratio r is an element of [1.5, 22.8]. Heat transport is analyzed by comparing the thermocapillary-enhanced process with that driven solely by conduction, and quantified by the enhancement ratio G, which simply compares melting times in each scenario. We find that G increases with phi ⢚ and r, and is maximum at an optimal heated length Ĩphi similar or equal to 0.5. Compared to previous works on the melting of n-octadecane in microgravity, the associated enhancement G is more moderate in this system, and oscillatory thermocapillary convection is not observed over the range of parameters explored.