We present experimental evidence of a transverse thermopower, or planar Nernst effect, in ferromagnetic metal thin films driven by thermal gradients applied in the plane of the films. Samples of 20 nm thick Ni and Ni(80)Fe(20) were deposited on 500 nm thick suspended Si-N thermal isolation platforms with integrated platinum strips designed originally to allow measurement of thermally generated spin currents (the spin Seebeck effect). The low thermal conductivity of the thin supporting Si-N structure results in an essentially 2D geometry that approaches the zero substrate limit, dramatically reducing the contribution of thermal gradients perpendicular to the sample plane typically found in similar experiments on bulk substrates. The voltage on the platinum strips generated transverse to the applied thermal gradient (V(T)) is linear with increasing ΔT and exhibits a sign reversal on hot and cold sides of the sample. However, V(T) is always even in applied magnetic field and shows a sinθ cosθ angular dependence, both key indicators of the planar Nernst effect. Within the 5 nV estimated error of our experiment there is no evidence of a signal from the spin Seebeck effect, which would have cosθ angular dependence, suggesting a reduced spin Seebeck coefficient in a planar, entirely thin-film geometry.