While the properties of standard (single-component) superfluids are well understood, principal differences arise in a special type of multicomponent systems - the so-called Borromean supercounterfluids - in which (i) supertransport is possible only in the counterflow regime and (ii) there are three or more counterflowing components. Borromean supercounterfluids's correlation and topological properties distinguish them from their single- and two-component counterparts. The component-symmetric case characterized by a distinctively different universality class of the supercounterfluid-to-normal phase transition is especially interesting. Using the recently introduced concept of compact-gauge invariance as the guiding principle, we develop the finite-temperature description of Borromean supercounterfluids in terms of an asymptotically exact long-wave effective action. We formulate and study Borromean XY and loop statistical models, capturing the universal long-range properties and allowing us to perform efficient worm algorithm simulations. Numeric results demonstrate perfect agreement with analytic predictions. Particularly instructive is the two-dimensional case, where the Borromean nature of the system is strongly manifested while allowing for an asymptotically exact analytic description.