We study the zero- and the finite-temperature behavior of the integrable spin-1/2 XXZ periodic chain with an impurity by the algebraic and thermal Bethe ansatz methods. We evaluate the impurity local magnetization at zero temperature analytically and derive the impurity susceptibility exactly from it. In the graphs of the impurity specific heat versus temperature, we show how the impurity spin becomes more liberated from the bulk many-body effect as the exchange coupling between the impurity spin and other spins decreases, and also that in low temperature it couples strongly to them such as the Kondo effect. Thus, we observe not only the crossover behavior from the high- to the low-temperature regime but also another one from the $N$-site chain to the $(N-1)$-site chain with a free impurity spin. We also show that the estimate of the Wilson ratio at a given low temperature is independent of the impurity parameter if its absolute value is small enough with respect to the temperature, and the universality class is described by the XXZ anisotropy in terms of the dressed charge.