  Thermal fluctuation in magnets will bring temperature-dependent self-energy
corrections to the magnons, however, their effects on the topological orders of
magnons is not well explored. Here we demonstrate that such corrections can
induce a Chern insulating phase in two-dimensional collinear antiferromagnets
with sublattice asymmetries by increasing temperature. We present the phase
diagram of the system and show that the trivial magnon bands at zero
temperature exhibit Chern insulating phase above a critical temperature before
the paramagnetic phase transition. The self-energy corrections close and reopen
the bandgap at {\Gamma} or K points, accompanied by a magnon chirality switch
and nontrivial Berry curvature transition. The thermal Hall effect of magnons
or detecting the magnon polarization can give experimentally prominent
signatures of topological transitions. We include the numerical results based
on van der Waals magnet MnPS3, calling for experimental implementation. Our
work presents a new paradigm for constructing topological phase that is beyond
the linear spin wave theory.
