  We numerically examine the transport of skyrmions driven over weak random
quenched disorder using a modified Thiele approach that includes the thermal
softening of skyrmion pairwise interactions introduced by Wang et al., Phys.
Rev. Appl. 18, 044024 (2022). The depinning transition is elastic at low
temperatures but becomes plastic with a reduced threshold at higher
temperatures due to the competition between thermal creep and thermal
softening, indicating a temperature-induced order to disorder transition into a
glass state. The resulting non-monotonic critical depinning forces and crossing
of the velocity-force curves are similar to what is observed in the peak effect
for type-II superconducting vortex lattices, where the softening of
vortex-vortex interactions with temperature leads to an order-disorder
transition. For low skyrmion densities the peak effect is absent since the
system is always in a disordered state. We map the dynamical phase transition
as a function of temperature, density, drive, and materials parameters, and
show that the signatures are similar to those of the superconducting peak
effect. Our results are consistent with recent experiments.
