Thermodynamical properties of the one-dimensional S=1/2 Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions, applicable to CuGeO 3 and Pb[Cu(SO 4 )(OH) 2 ] compounds, are studied by the numerically exact quantum transfer-matrix method. The Suzuki–Trotter formula is used to obtain a classical system with spin σ=3/2 and effective interactions between nearest neigbors only. Magnetic specific heat and magnetic susceptibility curves are calculated and compared with experimental results in a wide temperature range giving estimates of the coupling parameters in the model proposed for CuGeO 3 and Pb[Cu(SO 4 )(OH) 2 ].