Isolated kinks on thermally fluctuating 1/2 111 screw, 100 edge, and 1/2 111 edge dislocations in bcc iron are simulated under zero stress conditions using molecular dynamics (MD). Kinks are seen to perform stochastic motion in a potential landscape that depends on the dislocation character and geometry, and their motion provides fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier, and friction parameter are deduced from the simulations. A discrete Frenkel-Kontorova-Langevin model is able to reproduce the coarse-grained data from MD at ~10-7 of the computational cost, without assuming an a priori temperature dependence beyond the fluctuation- dissipationtheorem. Analytical results reveal that discreteness effects play an essential role in thermally activated dislocation glide, revealing the existence of a crucial intermediate length scale between molecular and dislocation dynamics. The model is used to investigate dislocation motion under the vanishingly small stress levels found in the evolution of dislocation microstructures in irradiated materials.