||We study the feasibility of using the "kernel approximation" to study finite temperature properties of strongly correlated electron systems. In this approximation, the density of eigenstates of a large Hermitian matrix is approximated by a truncated Chebyshev polynomial. Consequently some finite temperature properties of the physical system can be calculated numerically using this approximate density of state. Examples are the magnetic susceptibility and the specific heat. As a first example, we apply this method to calculate the temperature dependence of the magnetic susceptibility of Na9V14O35. We model this compound as a spin-l/2 Heisenberg model on a "ladder structure" with three different exchange interactions J1, J2, and J3. Best estimates for these three parameters are obtained by adjusting them and fitting the calculated magnetic susceptibility to experimental data. Using the optimized parameters, we study the specific heat and the spin gap of the compound. Our results indicate that Na9V14O35 is gapless. In the second example, we calculate the temperature dependence of the magnetic susceptibility of the one-hole t-J model. This is one of the most studied microscopic model in high temperature superconductivity. By performing the calculation on the 16- and 32-site square lattices with periodic boundary conditions, we can estimate the importance of finite size effects at different temperatures.