  Investigating the thermal inflationary model, we introduce stochastic
effects, incorporating a cutoff parameter $\sigma$ which distinguishes between
quantum and classical modes. Testing the model against Planck 2018 data, we
observe a preference for a non-zero $\sigma$ at least at 68\% C.L., suggesting
the classicalization of most modes and providing a theoretical foundation for
the quantum to classical transition. As a result of introducing the stochastic
effects, we find that the solution to the large-scale power deficit requires a
lower comoving temperature of inflaton.
