Ultrafast heating processes do not follow Fourier's heat conduction law, but rather the proposed Cattaneo-Vernotte equation (CVe) which has wave-like solutions that have some important differences from other wave phenomenon. In a periodic system made of materials with different thermal conductivities, solutions of the CVe lead to a band-like structure in the dispersion relation. In this work, we show that highly reflective Bragg mirrors for thermal waves can be designed. Even for a mirrors with a few layers a very high reflectance is achieved (>90%). The mirrors are made of materials with large thermal response times, where thermal waves have been measured. A second alternative consists of adding a thin metallic film which also leads to an efficient thermal Bragg mirror. Finally, the role of defects in opening new thermal-stop bands is demonstrated.