We have measured the attenuation of surface acoustic waves travelling through lithographied hybrid structures composed of MnAs thin films epitaxied on piezoelectric GaAs. Around room temperature, MnAs presents a well-known magnetostructural phase transition accompanied by a giant magnetocaloric effect. A large temperature dependent thermoelastic attenuation is found despite the film is much thinner (100 nm) than the wave penetration depth (similar to 10 mu m). This phenomenon is attributed to strain-induced triggering of the MnAs magneto-caloric effect. We find that the frequency (nu) dependence of attenuation is quite unusual, similar to nu(1.7), and that the attenuation weakly depends on the film thickness. We show that this behavior is due to the peculiar thermal boundary conditions imposed by magneto-caloric MnAs to the overall device. (C) 2014 AIP Publishing LLC.