We investigate nonlocal vortex motion in weakly pinning a-NbGe nanostructures, which is driven by a transport current I and remotely detected as a nonlocal voltage V(nl). At a high I of a given polarity, V(nl) changes sign dramatically. This is followed by V(nl) becoming even in I, with the opposite sign at low and high temperatures T. These findings can be explained by a Nernst-like effect resulting from local electron overheating (low T), and a magnetization enhancement due to a nonequilibrium quasiparticle distribution that leads to a gap enhancement near the vortex core (high T).