  Trace estimators allow to approximate thermodynamic equilibrium observables
with astonishing accuracy. A prominent representative is the finite-temperature
Lanczos method (FTLM) which relies on a Krylov space expansion of the
exponential describing the Boltzmann weights. Here we report investigations of
an alternative approach which employs Chebyshev polynomials. This method turns
out to be also very accurate in general, but shows systematic inaccuracies e.g.
produced by the smoothing kernel at low temperatures. Applications to
archetypical quantum spin systems are discussed as examples.
