  Wilson chains, based on a logarithmic discretization of a continuous
spectrum, are widely used to model an electronic (or bosonic) bath for Kondo
spins and other quantum impurities within the numerical renormalization group
method and other numerical approaches. In this short note we point out that
Wilson chains can not serve as thermal reservoirs as their temperature changes
by a number of order Delta E when a finite amount of energy Delta E is added.
This proves that for a large class of non-equilibrium problems they cannot be
used to predict the long-time behavior.
