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Electrical noise measurements at 10 Hz are reported for YBCO films at the resistive edge. Results are given for films with widths of 0.1, 1, and 5 mm that were deposited simultaneously on the same substrate, for three different substrate materials. The NET improves by approximately a factor of 10 as the thermometer area is increased by a factor of 2500, with fixed bias current, At temperatures giving maximum dR/dT and with nominally 19 mA bias currents, the 5 mm samples have very low noise equivalent temperatures of 3.1, 3.5, and 4.4 nK//spl radic/Hz for LaAlO/sub 3/, Al/sub 2/O/sub 3/, and Si substrates, respectively. These are the lowest values reported up to the present time. Surprisingly, noise from the sample on Si is consistent with pure Johnson noise even with bias Current as large as 5 mA (0.28/spl times/10/sup 4/ A/cm/sup 2/). For YBCO thicknesses no greater than 50 nm excellent thermometers can be made on any of these substrates in spite of the mechanical strains produced in the films by the substrate.