We investigate heat transport in a one-dimensional unpinned oscillator chain with stochastic momentum exchange, in contact with Langevin heat baths placed at both ends of the chain. While such a system is known to exhibit superdiffusive energy transport in the infinite-volume limit, a rigorous understanding of the corresponding boundary conditions has been lacking. We consider a finite chain of $n+1$ atoms, coupled at its endpoints to heat baths at temperatures $T_L$ and $T_R$, and study the evolution of the averaged energy profile under the superdiffusive time scale $t \mapsto n^{3/2} t$. We prove that, as $n \to \infty$, the empirical energy profile converges to the solution of a fractional heat equation driven by the Neumann fractional Laplacian $|\Delta|^{3/4}$ inside the interval $[0,1]$, with boundary boundary conditions determined by the temperatures of the heat baths. These conditions fix the temperatures at the endpoints of $[0,1]$. The limiting equation exhibits both a bulk Lévy-type superdiffusion and nonlocal boundary interactions, explicitly determined from the microscopic dynamics. Our analysis establishes the hydrodynamic limit without passing through an intermediate kinetic description, and clarifies the mechanism by which the microscopic Langevin reservoirs select the macroscopic boundary conditions in the superdiffusive regime. The results extend and complement previous work on infinite systems and highlight the contrast with pinned chains, where standard diffusive limits apply. Our talk is based on a joint work with Stefano Olla.