Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the su(2) algebra. A vibrational high-temperature partition function and the related thermodynamic potentials are derived in terms of the parameters of the model. Quantum analogues of anharmonic bosons, q bosons, are introduced and used to describe anharmonic properties of molecules and solids. It is shown that the quantum deformation parameter is related to the fixed number of anharmonic bosons and the shape of the anharmonic potential. A new algebraic realization of the q bosons, for the case of q being a root of unity, is given. This realization represents the symmetry of a linear lattice with periodic boundary conditions.