  We consider a simple system consisting of matter, radiation and vacuum
components to model the impact of thermal inflation on the evolution of
primordial perturbations. The vacuum energy magnifies the primordial modes
entering the horizon before its domination, making them potentially observable,
and the resulting transfer function reflects the phase changes and energy
contents. To determine the transfer function, we follow the curvature
perturbation from well outside the horizon during radiation domination to well
outside the horizon during vacuum domination and evaluate it on a constant
radiation density hypersurface, as is appropriate for the case of thermal
inflation. The shape of the transfer function is determined by the ratio of
vacuum energy to radiation at matter-radiation equality, which we denote by
$\upsilon$, and has two characteristic scales, $k_{\rm a}$ and $k_{\rm b}$,
corresponding to the horizon sizes at matter radiation equality and the
beginning of the inflation, respectively. If $\upsilon \ll 1$, the universe
experiences radiation, matter and vacuum domination eras and the transfer
function is flat for $k \ll k_{\rm b}$, oscillates with amplitude $1/5$ for $
k_{\rm b} \ll k \ll k_{\rm a}$ and oscillates with amplitude $1$ for $k \gg
k_{\rm a}$. For $\upsilon \gg 1$, the matter domination era disappears, and the
transfer function reduces to being flat for $k \ll k_{\rm b}$ and oscillating
with amplitude $1$ for $k \gg k_{\rm b}$.
