  We revisit the stellar cooling limits on the light scalar boson whose
coupling to the Standard Model particles is described by its mixing with the
Higgs boson. Strong constraints have been obtained from the electron-nucleus
bremsstrahlung process and the resonant plasma effect in the medium. We find
that the bremsstrahlung contribution from the electron and nucleus scattering
is of similar magnitude to the plasma mixing effect including the off-resonant
mixing. The constraints on the scalar coupling are found to be about three
orders of magnitude weaker than the previous evaluations. For white dwarfs, the
stellar cooling constraint is even more suppressed due to the Pauli blocking
effect. We obtain limits on the Higgs-scalar mixing angle of $10^{-10}-10^{-9}$
in the region where the scalar mass is lighter than about 10 keV.
