  We investigate thermodynamic properties of a one-dimensional S=1/2
antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum
Monte Carlo method. In particular we study how spin and lattice dimerize as a
function of the temperature, which gives a fundamental process of the
spin-Peierls transition in higher dimensions. The degree of freedom of the
lattice is taken into account adiabatically and the thermal distribution of the
lattice distortion is obtained by the thermal bath algorithm. We find that the
dimerization develops as the temperature decreases and it converges to the
value of the dimerization of the ground state at T=0. Furthermore we find that
the coupling constants of spins fluctuate quite largly at high temperature and
there thermodynamic properties deviate from those of the uniform chain. Doping
of non-magnetic impurities causes cut of the chain into short chains with open
boundary. We investigate thermodynamic properties of open chains taking
relaxation of the lattice into consideration. We find that strong bonds locate
at the edges and a defect of the bond alternation appears in the chain with odd
number of sites, which causes enhancement of the staggered magnetic order. We
find a spreaded staggered structure which indicates that the defect moves
diffusively in the chain even at very low temperature.
