On cooling from the melt, plutonium (Pu) undergoes a series of structural transformations accompanied by a ≈ 28% reduction in volume from its
δ
phase to its
α
phase at low temperatures. While Pu’s partially filled 5
f
-electron shells are known to be involved, their precise role in the transformations has remained unclear. By using calorimetry measurements on
α
-Pu and gallium-stabilized
δ
-Pu combined with resonant ultrasound and X-ray scattering data to account for the anomalously large softening of the lattice with temperature, we show here that the difference in electronic entropy between the
α
and
δ
phases dominates over the difference in phonon entropy. Rather than finding an electronic specific heat characteristic of broad
f
-electron bands in
α
-Pu, as might be expected to occur within a Kondo collapsed phase in analogy with cerium, we find it to be indicative of flatter subbands. An important role played by Pu’s 5
f
electrons in the formation of its larger unit cell
α
phase comprising inequivalent lattice sites and varying bond lengths is therefore suggested.