This paper reports high resolution X-ray photoelectron spectroscopy (XPS) studies on Fe$_{1-x}$Ni$_x$ (x=0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.9) alloys down to 10 K temperature. Core levels and Auger transitions of the alloys except the invar alloy (x=0.4) exhibit no observable temperature induced changes. The invar alloy exhibits changes in the core levels below 20 K temperature that strongly depend on the core level. Such core level dependent changes with temperature were attributed to the precipitation of spin glass like phase below 20 K only in the invar alloy. Ni L$_3$M$_{45}$M$_{45}$ Auger transition also supported such precipitation below 20 K.