Migration of nanosized liquid Pb inclusions attached to dislocations in Al has been observed during in-situ transmission electron microscopy heating experiments and monitored by real-time video recordings. The movements of the inclusions can be separated into two independent components parallel to and perpendicular to the dislocations respectively. Movements parallel to the dislocation lines display properties of partially confined one-dimensional random walks where smaller inclusions can be seen to move over distances that are many times their own sizes. In contrast, the trajectories perpendicular to the dislocation lines are within narrowly confined spaces. Frame-by-frame analysis of digitized video sequences recorded at different temperatures for the same inclusion attached to a nearly horizontal dislocation illustrates the two types of movement. The step lengths parallel to the dislocation increase rapidly with increasing temperature while the step lengths in the transverse movement only display a weak temperature dependence. A detailed statistical analysis of the inclusion trajectories documents that both patterns of movement are random. The activation enthalpy of the one-dimensional movement parallel to the dislocation was found to be 2.72 +/- 0.10 eV at lower temperatures and 1.44 +/- 0.07 eV at higher temperatures with a transition temperature around 650-660 K.