Lead halide perovskites possess unique characteristics well‐suited for optoelectronic and energy capture devices, however, concerns about their long‐term stability remain. All‐inorganic CsPbX3 (X = Cl, Br, I) perovskite nanocrystals have been reported with improved stability. We investigate the photo‐ and thermal‐stability properties of CsPbX3 (X = Cl, Br, I) nanocrystals by electron microscopy, x‐ray diffraction, thermogravimetric analysis, ensemble and single particle spectral characterization. CsPbBr¬3 is stable under 1‐sun illumination for 16 h in ambient conditions, although single crystal analysis indicates the luminescence states change over time. CsPbBr¬3 is also stable to heating to 250 °C. Large CsPbI3 crystals (34 ± 5 nm) are the least stable under the same conditions; and with heating, the γ (black) phase reverts to the non‐luminescent δ phase. Smaller CsPbI3 nanocrystals (14 ± 2 nm) purified by a different washing strategy exhibit improved photostability with no evidence of crystal growth but are still thermally unstable. Both CsPbCl3 and CsPbBr3 show crystal growth under irradiation or heat, likely with a preferential orientation. TGA‐FTIR reveals nanocrystal mass loss was only from liberation and subsequent degradation of surface ligands. Encapsulation or other protective strategies should be employed for long‐term stability under conditions of high irradiance or temperature.