  In contact Hamiltonian systems, the so-called dissipated quantities are akin
to conserved quantities in classical Hamiltonian systems. In this paper, we
prove a Noether's theorem for non-autonomous contact Hamiltonian systems,
characterizing a class of symmetries which are in bijection with dissipated
quantities. We also study other classes of symmetries which preserve (up to a
conformal factor) additional structures, such as the contact form or the
Hamiltonian function. Furthermore, making use of the geometric structures of
the extended tangent bundle, we introduce additional classes of symmetries for
time-dependent contact Lagrangian systems. Our results are illustrated with
several examples. In particular, we present the two-body problem with
time-dependent friction, which could be interesting in celestial mechanics.
