Thermal inflation is a second epoch of exponential expansion at typical energy scales V-1/4 similar to 10(6 similar to 8) GeV. If the usual primordial inflation is followed by thermal inflation, the primordial power spectrum is only modestly redshifted on large scales, but strongly suppressed on scales smaller than the horizon size at the beginning of thermal inflation, k > k(b) = a(b)H(b). We calculate the spectral distortion of the cosmic microwave background generated by the dissipation of acoustic waves in this context. For k(b) << 10(3) Mpc(-1), thermal inflation results in a large suppression of the mu-distortion amplitude, predicting that it falls well below the standard value of mu similar or equal to 2 x 10(-8). Thus, future spectral distortion experiments, similar to PIXIE, can place new limits on the thermal inflation scenario, constraining k(b) greater than or similar to 10(3) Mpc(-1) if mu similar or equal to 2 x 10(-8) were found.
