The finite-temperature Casimir effect for a scalar field in the bulk region of two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation a on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attraction versus repulsion of the temperature correction to the force is discussed in the special cases of Dirichlet-Dirichlet, Neumann-Neumann and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is used, as this is found to be the most convenient. Some comments are made on the related contemporary literature.