Is the pyrolysis of tetrachloroaluminate(III) anion possible?
Unlike lithium tetrafluoroborate $\ce{LiBF4},$ sodium tetrachloroaluminate $\ce{NaAlCl4}$ doesn't decompose upon melting, and doesn't show any signs of decomposition or phase transition up to approx. $\pu{800 °C}$ [1, p. 688]:


FIGURE 3. Calculated $(\ce{NaCl + AlCl3})$ phase diagram at $\pu{0.1 MPa}$ (dotted lines are liquid–liquid miscibility gap boundary and monotectic at $P &gt; \pu{0.1 MPa}).$

Molten sodium tetrachloroaluminate is used as electrolyte in ZEBRA batteries with normal operating temperature range of $\pu{270–350 °C}.$
References

Robelin, C.; Chartrand, P.; Pelton, A. D. Thermodynamic Evaluation and Optimization of the $(\ce{NaCl + KCl + AlCl3})$ System. The Journal of Chemical Thermodynamics 2004, 36 (8), 683–699. https://doi.org/10.1016/j.jct.2004.04.011.