Persistent, weak-banded electrostatic emissions with &mgr; V/m amplitudes have been observed in the magnetosphere at frequencies between the electron gyrofrequency &ohgr;cc and upper hybrid frequency &ohgr;uh when &ohgr;cc<&ohgr;uh. The suggestion that these low-level emissions are thermal fluctuations is qualitatively explored by using a simple hot-cold model for dayside electron distributions with density and temperature ratios nc/nh≫1 and Th/Tc≫1. We conclude that for typical dayside conditions the observed waves are weakly damped Bernstein--Harris modes whose spectral density (E2(f)) ~10-16V2/m2-Hz and polarization perpendicular to the ambient magnetic field can be accounted for by the theory. The electrostatic power spectrum of the waves scales as &ohgr;cc2Th/Tc3/2 for a Maxwellian hot component but may be enhanced considerably for the case of marginally stable or nonconvective modes. Wavelengths scale as the cold electron gyroradius &rgr;c so that significant attenuation of the measured spectrum may occur when measurements are made with antennas of characteristics lengths l~&rgr;c. Representative fluctuations spectrums are computed for dayside synchronous orbit by using typical hot-cold plamsa parameters and hypothetical dipole antenna lengths of 50 and 100 m. It is suggested that the formalism developed here may be applicable to weak electron cyclotron emissions at Jupiter and Saturn and may be extended to lower-frequency ion cyclotron fluctuations by modifying the theory to include ion contributions.