Spin wave dispersion in the metallic antiferromagnet Mn$_3$Pt was investigated just above the order-order transition temperature by using the inelastic neutron scattering technique. The spin wave dispersion at $T = 400$ K along [100], [110] and [111] directions was isotropic within the measurement accuracy. The dispersion was described by $({hbaromega})^2 = c^2q^2 + Delta^2$ with $c = 190$ meV {AA} and $Delta = 3.3$ meV. Compared with the dispersion at $T = 419$ K previously reported, the result demonstrates a large reduction of the stiffness constant $c$ with increasing temperature. This is similar to that observed in the metallic antiferromagnet FePt$_3$, and is an indication of the itinerancy of the magnetic moments.
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