  The effect of thermal phase fluctuations (TPF's) on the ab-plane penetration
depth, lambda(T), of thin YBa2Cu3O(7-delta) (YBCO) films is found to be much
smaller than expected from the paradigm of cuprates as weakly-coupled 2D
superconducting layers. A 2D vortex-pair-unbinding transition is observed, but
the effective thickness for fluctuations is the film thickness, not a CuO
bilayer thickness. In a strongly underdoped YBCO film, Tc= 34 K, TPF's suppress
Tc by only about 3 K. They cannot be a significant factor in the suppression of
Tc and emergence of the pseudogap with underdoping.
