  Imperfections in correlated materials can alter their ground state as well as
finite-temperature properties in significant ways. Here, we develop a method
based on numerical linked-cluster expansions for calculating exact
finite-temperature properties of disordered lattice models directly in the
thermodynamic limit. We show that a continuous distribution for disordered
parameters can be achieved using a set of carefully chosen discrete modes in
the distribution, which allows for the averaging of properties over all
disorder realizations. We benchmark our results for thermodynamic properties of
the square lattice Ising and quantum Heisenberg models with bond disorder
against Monte Carlo simulations and study them as the strength of disorder
changes. We also apply the method to the disordered Heisenberg model on the
frustrated checkerboard lattice, which is closely connected to
Sr$_2$Cu(Te$_{0.5}$W$_{0.5}$)O$_6$. Our method can be used to study
finite-temperature properties of other disordered quantum lattice models
including those for interacting lattice fermions.
