Performing Monte Carlo simulations, we study the temperature-dependent self-organization of magnetic moments coupled to itinerant electrons in a finite-size one-dimensional nanostructure proximitized to a superconducting reservoir. At low temperatures, an effective interaction between the localized magnetic moments, that is mediated by itinerant electrons, leads to their helical ordering. This ordering, in turn, affects the itinerant electrons and can induce the topologically nontrivial superconducting phase with Majorana edge modes. I will show that in a wide range of system parameters, the spatial periodicity of a spiral order that minimizes the ground-state energy turns out to promote the topological phase. Moreover, despite the one-dimensional geometry of the system, the topological state survives at elevated temperatures.
