Ultrashort period planets offer a window into the poorly understood interior composition of exoplanets through material evaporated from their rocky interiors. Among these objects are a class of disintegrating planets, observed when their dusty tails transit in front of their host stars. These dusty tails are thought to originate from dust condensation in thermally driven winds emanating from the sublimating surfaces of these planets. Existing models of these winds have been unable to explain their highly variable nature and have not explicitly modelled how dust forms in the wind. Here, we present new radiation-hydrodynamic simulations of the winds from these planets, including a minimal model for the formation and destruction of dust, assuming that nucleation can readily take place. We find that dust forms readily in the winds, a consequence of large dust grains obtaining lower temperatures than the planet's surface. As hyphothesized previously, we find that the coupling of the planet's surface temperature to the outflow properties via the dust's opacity can drive time-variable flows when dust condensation is sufficiently fast. In agreement with previous work, our models suggest that these dusty tails are a signature of catastrophically evaporating planets that are close to the end of their lives. Finally, we discuss the implications of our results for the dust's composition.