Our inelastic neutron scattering study of spin excitations in iron telluride reveals remarkable thermal evolution of the collective magnetism. In the temperature range relevant for the superconductivity in FeTe(1-x)Se(x) materials, where the local-moment behavior is dominated by liquidlike correlations of emergent spin plaquettes, we observe unusual, marked increase of magnetic fluctuations upon heating. The effective spin per Fe at T ≈ 10 K, in the phase with weak antiferromagnetic order, corresponds to S ≈ 1, consistent with the recent analyses that emphasize importance of Hund's coupling [K. Haule and G. Kotliar, New J. Phys. 11, 025021 (2009).]. However, it grows to S ≈ 3/2 in the high-T disordered phase, suggestive of the Kondo-type behavior, where local magnetic moments are entangled with the itinerant electrons.