The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature, of which the leading contributor is the blackbody radiation (BBR) shift. Experimental measurements of the BBR shifts are difficult. In this work, we have calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in Rb-87 using the relativistic all-order method and carried out a detailed evaluation of the accuracy of our final value. Particular care is taken to accurately account for the contributions from highly excited states. Our predicted value for the Stark coefficient, k(S) = -1.240(4) x 10(-10) Hz/(V/m)(2), is three times more accurate than the previous calculation [E.J. Angstman, V.A. Dzuba, and V.V. Flambaum, Phys. Rev. A 74, 023405 (2006)].