  Weyl semimetals are arguably the most paradigmatic form of a gapless
topological phase. While the stability of Weyl nodes, as quantified by their
topological charge, has been extensively investigated, recent interest has
shifted to the manipulation of the location of these Weyl nodes for non-Abelian
braiding. To accomplish this braiding it is necessary to drive significant Weyl
node motion using realistic experimental parameter changes. We show that a
family of phase transitions characterized by certain symmetry constraints
impose that the Weyl nodes have to reorganise by a large amount, shifting from
one high symmetry plane to another. Additionally, for a subset of pairs of
nodes with nontrivial Euler class topology, this reorganization can only occur
through a braiding process with adjacent nodes. As a result, the Weyl nodes are
forced to move a large distance across the Brillouin zone and to braid, all
driven by small temperature changes, a process we illustrate with
Cd$_2$Re$_2$O$_7$. Our work opens up routes to readily manipulate Weyl nodes
using only slight external parameter changes, paving the way for the practical
realization of reciprocal space braiding.
