Two-component ionogels containing clay minerals such as montmorillonite K10 (Mnt-K10), bentonite (Bent), and halloysite (Hly), as well as imidazolium-based ionic liquids (ILs) were prepared in present work. The ILs that were used in the synthesis included a bis(trifluoromethylsulfonyl) imide anion (TFSI-) and various cations: 1-ethyl-3-methylimidazolium (EMIm+), 1-propyl-3-methylimidazolium (PMIm+), 1-butyl-3-methylimidazolium (BMIm+), and 1-butyl-2,3-dimethylimidazolium (BDMIm+). The thermal behavior of the synthesized ionogels and neat ILs was investigated using differential scanning spectroscopy (DSC) and thermogravimetric analysis (TG). It was found that the thermograms of PMImTFSI, BMImTFSI, and BDMImTFSI showed inflections corresponding to glass-transition, which shifted towards higher temperatures with the introduction of aluminosilicate. The largest shifts compared to the neat ILs were observed for IL/Bent ionogels. It was assumed that the identified differences in the thermal behavior between the neat and clay-entrapped ILs (confinement effect) are associated with an increased role of ion-wall interactions compared to ion-ion interactions. When studying the thermal stability of the materials under consideration, two opposite trends were noted. On the one hand, the characteristic temperatures of thermal decomposition of the synthesized ionogels were lower than those for the neat ILs. But on the other hand, when introducing aluminosilicate into any IL, a decrease in the maximum rate of thermal decomposition was observed in accordance with series of IL > IL/Mnt-K10 > IL/Hly > IL/Bent.