<p>A thermo-elastic continuum model for a mass-in-mass metamaterial is suggested. An influence of thermal conduction on the harmonic wave behaviour is studied using an asymptotic dispersion relation analysis. It is found that the position and the size of the band gap is not affected by the thermal effects. Numerical simulations are performed on boundary excitation of thermo-elastic waves using both the harmonic and constant temperature excitations. Mutual influence of the strain and thermal waves give rise to oscillatory or monotonically decaying wave profiles.</p>