In order to model quasi-one-dimensional magnetic systems such as CuGeO3, we need to be able to calculate various properties of one-dimensional quantum lattice models. White's density matrix renormalisation group (DMRG) method has proven to be highly successful for calculating low-energy properties of such systems. However, in order to make direct comparisons with experiment, we require properties of the system at non-zero temperature. Using a recent adaptation of the DMRG to two-dimensional IRF models and the Trotter-Suzuki map between one-dimensional quantum and two-dimensional classical systems, we have applied the DMRG to the calculation of thermodynamic properties of a quantum spin chain at non-zero temperature. Here we discuss an improved density matrix which leads to a marked increase in the accuracy of the calculated free energy.