  If inflation scale is high, light scalars acquire large quantum fluctuations
during inflation.If sufficiently long-lived, they will give rise to CDM
isocurvature perturbations, which are highly constrained by the Planck data.
Focusing on string axions as such light scalars, we show that thermal inflation
can provide a sufficiently large entropy production to dilute the CDM
isocurvature perturbations. Importantly, efficient dilution is possible for the
string axions, because effectively no secondary coherent oscillations are
induced at the end of thermal inflation, in contrast to the moduli fields. We
also study the viability of the axion dark matter with mass of about 7 keV as
the origin of the 3.5 keV X-ray line excess, in the presence of large entropy
production.
