  We consider the impact of thermal inflation -- a short, secondary period of
inflation that can arise in supersymmetric scenarios -- on the stochastic
gravitational wave background. We show that while the primordial inflationary
gravitational wave background is essentially unchanged at CMB scales, it is
massively diluted at solar system scales and would be unobservable by a BBO
style experiment. Conversely, bubble collisions at the end of thermal inflation
can generate a new stochastic background. We calculate the likely properties of
the bubbles created during this phase transition, and show that the expected
amplitude and frequency of this signal would fall within the BBO range.
