Thermodynamic Derivation of Wien's Law?

Can someone tell me how I can derive Wien's law, i.e.,

[itex]\lambda_{max} T = constant[/itex]

where [itex]\lambda_{max}[/itex] is the peak wavelength and [itex]T[/itex] is the absolute temperature of the black body, using the equation,

[itex]P=\frac{U^{*}}{3}[/itex]

where [itex]U^{*}[/itex] is the energy density.

Note: I'm not looking for the derivation using Plank's formula. I'm looking for a purely thermodynamic derivation.

Thanks in advance!!