We examine a U(1)-symmetric field theory for two scalar fields in which the tree-level potential is unbounded from below. We calculate the finite-temperature effective potential and demonstrate that (1) radiative corrections stabilize the theory; (2) Q-balls appear at low temperatures: and (3) the U(1) symmetry is spontaneously broken at high temperatures and restored at low temperatures. We investigate the theory's dynamics in a sector of fixed charge, focusing on the cosmological production of Q-balls as relics of the early era of broken symmetry.