Using the full nonlinear Ginzburg-Landau equations, we study the behaviour of a particular superconducting micronetwork near its transition temperature: a circular loop connected to an infinitely long wire by a branch of length L. In this mesoscopic structure the superconducting condensate is confined by the boundary conditions, leading to nonlocal current effects. When a current i_w is flowing in the infinitely long wire, the current i_ℓ in the loop can be found by numerical methods. This allows us to determine the relationship between the critical current i_c in the loop, at which superconductivity disappears, and the current i_w. When i_w is zero or small compared to the critical current, decreasing L increases i_c, while increasing i_w decreases i_c more rapidly for the smaller L values. As the temperature is raised, i_c occurs at smaller and smaller magnetic flux in the loop. When the loop is positioned in such a way that no magnetic flux from the current in the wire is coupled to the loop, the current in the loop is still modified through the superconducting condensate in the branch.