Despite recent successes in the synthesis of boron nanotubes (BNTs), the atomic arrangement of their walls has not yet been determined and many questions about their basic properties remain. Here, the dynamic stability of BNTs is unveiled by means of first-principles molecular dynamics simulations. Free-standing, single-wall BNTs with diameters larger than 0.6 nm are found to be thermally stable at the experimentally reported synthesis temperature of 870 C and higher. The walls of thermally stable BNTs are found to have a variety of different mixed triangular-hexagonal morphologies. These results substantiate the importance of mixed triangular-hexagonal morphologies as a structural paradigm for atomically thin boron.