  We study the effect of mesoscopic fluctuations on the validity of the
Wiedemann--Franz (WF) law for quasi-one-dimensional metal wires and open
quantum dots. At temperatures much less than the generalized Thouless energy,
E_c, the WF law is satisfied for each specific sample but as the temperature is
raised through E_c a sample-specific correction to the WF law of order 1/g
appears (g is the dimensionless conductance) and then tends to zero again at
high temperatures. The mesoscopic violation of the Weidemann-Franz law is even
more pronounced in a ring geometry, for which Lorenz number exhibits h/e
flux-periodic Aharonov-Bohm oscillations.
