We discuss the cosmology of models in which the standard model Yukawa couplings depend on scalar field(s), often referred to as flavons. We find that thermal corrections of the flavon potential tend to decrease the Yukawa couplings, providing an important input to model-building. Working in the specific framework of Froggatt-Nielsen models, we compute the abundance of flavons in the early universe generated both via freeze-in and from coherent oscillations induced by thermal corrections to their potential, and discuss constraints on flavon models from cosmology. We find that cosmology places important constraints on theories containing flavons even for regions of parameter space inaccessible to collider searches.