A method is developed to Calculate the finite-temperature infrared absorption spectrum of polyatomic molecules with energy levels described by a second-order Dunham expansion. The anharmonic couplings are fully incorporated in the calculation of the quantum density of states, achieved using a Wang-Landau Monte Carlo procedure, as well as in the determination of transition energies. Additional multicanonical simulations provide the microcanonical absorption intensity as a function of both the absorption wavelength and the internal energy of the molecule. The finite-temperature spectrum is finally obtained by Laplace transformation of this microcanonical histogram. The present scheme is applied to the infrared spectrum of naphthalene, for which we quantity the shifting, broadening, and third-order effects as a continuous function of temperature. The influence of anharmonicity and couplings is manifested on the nontrivial variations of these features with increasing temperature.