The finite-temperature transport properties of FeRh compounds are investigated by first-principles density-functional-theory-based calculations. The focus is on the behavior of the longitudinal resistivity with rising temperature, which exhibits an abrupt decrease at the metamagnetic transition point, T = T-m, between ferro-and antiferromagnetic phases. A detailed electronic structure investigation for T >= 0 K explains this feature and demonstrates the important role of (i) the difference of the electronic structure at the Fermi level between the two magnetically ordered states and (ii) the different degree of thermally induced magnetic disorder in the vicinity of T-m, giving different contributions to the resistivity. To support these conclusions, we also describe the temperature dependence of the spin-orbit-induced anomalous Hall resistivity and Gilbert damping parameter. For the various response quantities considered, the impact of thermal lattice vibrations and spin fluctuations on their temperature dependence is investigated in detail. Comparison with corresponding experimental data shows, in general, very good agreement.