I am assuming that the composition that you specified is in mass %, and NOT mole %. Converted to mole % for the Al2O3-SiO2 binary system the composition is about 63.87% Al2O3 and 36.13% SiO2. You can use that to read off the binary diagram that you can find here:
The system is fully solid at 1800 C, and fully liquid at 1900 C. You can use FactSage (www.factsage.com) to get more detailed information that incorporates Fe2O3, K2O, and Na2O.
The stability of the material as a function of temperature is just one consideration. The material that you will contain with the refractory material is just as important, since it can flux the refractory and create a low melting point composition.
The chemical composition of this brick is similar to mullite. A typical mullite softening point around 1800 C. Near this temperature is likely to create cone. However, mineralogical composition should be considered. Only chemical analysis is not enough to predict ceramic material.