We investigate the mobility of screw dislocations decorated by carbon solutes in body-centered cubic iron based on density functional theory (DFT) calculations and transmission electron microscopy (TEM) observations of in-situ straining experiments. We focus on the high-temperature domain, between 500 and 800 K, where plasticity is controlled by the slow glide of decorated screw dislocations with a mobility similar to the Peierls mechanism existing below 300 K, at variance with the athermal regime observed at intermediate temperatures. We propose that due to the strong pinning of reconstructed dislocation lines by carbon solutes, dislocation glide occurs by the formation and migration of kinks, both controlled by the jumps of carbon atoms. We calculate the associated kink-pair nucleation and formation energies as well as the migration energies of isolated kinks and use these DFT values to predict the dislocation velocity as a function of temperature, applied stress and dislocation length. The validity of the mobility law is assessed by the comparison with dislocation velocities measured in TEM observations at different temperatures and local shear stresses. The quantitative agreement between the experimental measurements and the analytical model supports the proposed glide mechanism and the DFT values obtained for kink energies.