  Current estimates of number counts of radio sources in the frequency range
where the most sensitive Cosmic Microwave Background (CMB) experiments are
carried out significantly under-represent sources with strongly inverted
spectra. Hot accretion flows around supermassive black holes in the nuclei of
nearby galaxies are expected to produce inverted radio spectra by thermal
synchrotron emission. We calculate the temperature fluctuations and power
spectra of these sources in the Planck Surveyor 30 GHz energy channel, where
their emission is expected to peak. We find that their potential contribution
is generally comparable to the instrumental noise, and approaches the CMB
anisotropy level at small angular scales. Forthcoming CMB missions, which will
provide a large statistical sample of inverted-spectra sources, will be crucial
for determining the distribution of hot accretion flows in nearby quiescent
galactic nuclei. Detection of these sources in different frequency channels
will help constrain their spectral characteristics, hence their physical
properties.
