Mounting evidence suggests that planned and present gravitational-wave detectors may be sensitive to signatures from first-order phase transitions in the early universe. Here, we consider the recently-proposed \enquote{flavour transfer} model, where the Standard Model flavour structure is augmented by a new horizontal SU(2) flavour gauge group. For such a model, the new gauge symmetry is broken far above the electroweak scale and constraints are dominated by \enquote{flavour-transfer} operators rather than flavour-changing currents. We calculate the finite-temperature corrections to the effective potential and determine the critical temperature at which we expect a phase transition. We examine the parameters for which the phase transition is strongly first order.