We apply the transfer-matrix density matrix renormalization group (DMR
G) approach to frustrated quantum spin chains, down to T = 0.025 K in
the thermodynamic limit. The incommensurability problem of exact diago
nalization and the negative sign problem of quantum Monte Carlo vanish
completely. For illustration, we give results for chains with next-ne
arest-neighbor frustration and for the delta chain, which has been a t
estbed for many thermodynamic methods. The DMRG approach proves to be
an extremely powerful method for the old problem of the thermodynamics
of frustrated systems.