The blackbody-radiation (BBR) shift of the 5s-4d(5/2) clock transition in Sr-88(+) is calculated to be 0.250(9) Hz at room temperature, T = 300 K, using the relativistic all-order method where all single and double excitations of the Dirac-Fock wavefunction are included to all orders of perturbation theory. The BBR shift is a major component in the uncertainty budget of the optical frequency standard based on the Sr-88(+) trapped ion. The scalar polarizabilities of the 5s and 4d(5/2) levels, as well as the tensor polarizability of the 4d(5/2) level, are presented together with the evaluation of their uncertainties. The lifetimes of the 4d(3/2), 4d(5/2), 5p(1/2) and 5p(3/2) states are calculated and compared with experimental values.