A computation is given of the fluctuations in average temperature of an isolated thin film on a substrate, the noise being due to two causes: (i) fluctuations in blackbody radiation absorbed and emitted by the front surface; (ii) thermal diffusion in the sample and the substrate. The surface source results in a large 1/frange, the level of which decreases with increasing heat conductivity of the substrate; the noise goes over into a 1/f2spectrum at high frequencies. The noise due to the volume source results in a 1/f1/2spectrum, going over into a 1/f3/2spectrum at higher frequencies; the noise also decreases with increasing heat conductivity of the substrate. The integrated total noise is of the orderkT20/C. Under most circumstances the spectrum due to the volume source dominates.