  Quantized particle or spin transport upon cyclic parameter variations,
determined by topological invariants, is a key signature of Chern insulators in
the ground state. While measurable many-body observables exist that preserve
the integrity of topological invariants also at finite temperature, quantized
transport is generically lost. We here show that a coupling of a
one-dimensional Chern insulator at arbitrary finite temperature to an auxiliary
lattice can induce quantized transport determined by the finite-temperature
invariant. We show for the example of a Rice-Mele model that the spatial
distribution of a single particle in the auxiliary chain moves by a quantized
number of unit cells in a Thouless cycle when subtracting a spatially
homogeneous offset even at a temperature exceeding the band gap.
