  Engineering new quantum phases requires fine tuning of the electronic,
orbital, spin, and lattice degrees of freedom. To this end, the kagome lattice
with flat bands has garnered great attention by hosting various topological and
correlated phases, when the flat band is at the Fermi level. Here we discover
unconventional nematiciy in kagome metal CoSn, where flat bands are fully
occupied below the Fermi level. Thermodynamic, dilatometry, resonant X-ray
scattering, inelastic neutron scattering, Larmor diffraction, and
thermoelectric measurements consistently hint at rotational symmetry-breaking
and nematic order that is pronounced only near T=225 K. These observations,
principally the nematic's finite temperature stability -- incipience -- can be
explained by a phenomenological model which reveals that thermally excited flat
bands promote symmetry breaking at a characteristic temperature. Our work shows
that thermal fluctuations, which are typically detrimental for correlated
electron phases, can induce new ordered states of matter, avoiding the
requirements for fine tuning of electronic bands.
