  The low temperature thermodynamics of correlated 1D fermionic models with
spin and charge degrees of freedom is obtained by exact diagonalization (ED) of
small systems and followed by density matrix renormalization group (DMRG)
calculations that target the lowest hundreds of states $\{E(N)\}$ at system
size $N$ instead of the ground state. Progressively larger $N$ reaches $T <
0.05t$ in correlated models with electron transfer $t$ between first neighbors
and bandwidth $4t$. The size dependence of the many-fermion basis is explicitly
included for arbitrary interactions by scaling the partition function. The
remaining size dependence is then entirely due to the energy spectrum
$\{E(N)\}$ of the model. The ED/DMRG method is applied to Hubbard and extended
Hubbard models, both gapped and gapless, with $N_e = N$ or $N/2$ electrons and
is validated against exact results for the magnetic susceptibility $\chi(T)$
and entropy $S(T)$ per site. Some limitations of the method are noted. Special
attention is given to the bond-order-wave phase of the extended Hubbard model
with competing interactions and low $T$ thermodynamics sensitive to small gaps.
