  Quasi-conformal models are an appealing scenario that can offer naturally a
strongly supercooled phase transition and a period of thermal inflation in the
early Universe. A crucial aspect for the viability of these models is how the
Universe escapes from the supercooled state. One possibility is that thermal
inflation phase ends by nucleation and percolation of true vacuum bubbles. This
route is not, however, always efficient. In such case another escape mechanism,
based on the growth of quantum fluctuations of the scalar field that eventually
destabilize the false vacuum, becomes relevant. We study both of these cases in
detail in a simple yet representative model. We determine the duration of the
thermal inflation, the curvature power spectrum generated for the scales that
exit horizon during the thermal inflation, and the stochastic gravitational
wave background from the phase transition. We show that these gravitational
waves provide an observable signal from the thermal inflation in almost the
entire parameter space of interest. Furthermore, the shape of the gravitational
wave spectrum can be used to ascertain how the Universe escaped from
supercooling.
