The structure of confined two-dimensional systems of dust particles in dusty plasmas is analyzed at finite temperatures by numerical simulations and theoretical approaches. The finite Yukawa system is adopted as a model for these systems and the variational method which has been successful in reproducing structures at low temperatures is extended to finite temperatures through replacement of the cohesive energy by the Helmholtz free energy recently given in the form of simple interpolation formulas. The results are compared with those of numerical simulations and their satisfactory agreement has been obtained. Finite-temperature structures presented here will be useful to evaluate the physical parameters of the two-dimensional systems of dust particles often formed near the boundary between the plasma bulk and the sheath.