  It is shown that White's density matrix renormalization group technique can
be adapted to obtain thermodynamic quantities. As an illustration, the magnetic
susceptibility of Heisenberg S=1/2 and S=3/2 spin chains are computed. A
careful finite size analysis is made to determine the range of temperatures
where the results are reliable. For the S=1/2 chain, the comparison with the
exact Bethe ansatz curve shows an agreement within 1% down to T=0.05J.
