We study the propagation of the normal-superfluid interface under inhomogen
eous cooling. Assuming a uniform temperature gradient we establish the cond
itions for creating topological defects for both slow and fast superfluid t
ransitions using the time-dependent Ginzburg-Landau theory. For fast transi
tions, we find agreement with the Kibble-Zurek scenario. Experiments where
the temperature change is generated by absorption of a neutron in He-3 are
discussed.