The potential profile in the vicinity of the throat of a tandem-mirror thermal-barrier cell is studied. A model ion distribution function which resembles that obtained from numerical Fokker-Planck code studies is used. For all but very small ratios of trapped- to passing-particle densities, the self-consistent potential satisfies quasi-neutrality and varies gradually between its value just beyond the throat and a depressed value in the interior of the barrier cell. As the trapped-particle density decreases, a sheath develops at a finite distance from the mirror throat. For still lower trapped-particle densities, the throat region ceases to be quasineutral; the solution to Poisson's equation is a sheath-like structure whose height depends on the net charge density at the throat, which, in turn, is determined by the requirement that the solution match smoothly to the profile in the adjacent cell.