MAX phases have great potential under demands of both high-temperature and high-stress performance, with their mixed atomic bonding producing the temperature and oxidation resistance of ceramics with the mechanical resilience of metals. Here, we measure the mechanical properties up to 980C by nanoindentation on highly dense and pure Cr$_2$AlC, as well as after oxidation with a burner rig at 1200C for more than 29 hours. Only modest reductions in both hardness and modulus up to 980C were observed, implying no change in deformation mechanism. Furthermore, micro-cantilever fracture tests were carried out at the Cr$_2$AlC/Cr$_7$C$_3$ and Cr$_7$C$_3$/Al$_2$O$_3$ interfaces after the oxidation of the Cr$_2$AlC substrates with said burner rig. The values are typical of ceramic-ceramic interfaces, below 4 MPa/m, leading to the hypothesis that the excellent macroscopic behaviour is due to a combination of low internal strain due to the match in thermal expansion coefficient as well as the convoluted interface.