Structure of nanofillers and their subsequent interaction with a polymer is very important in determining thermal stability of polymer nanocomposite. In this paper, we tried to correlate structure of various 0, 1 and 2 dimensional nanofillers with the thermal stability of hydrogenated nitrile butadiene rubber (HNBR) nanocomposites. Organically modified and unmodified layered silicates such as montmorillonite (Cloisite Na+, Cloisite 30B and Cloisite 15A), rod-like fibrous filler (sepiolite) and spherical nanoparticles (nanosilica) were chosen for this purpose. A significant improvement in thermal stability (obtained by thermogravimeric analysis and differential scanning calorimetry) was observed for silica-filled nanocomposites. However, the activation energy of the nanocomposites calculated by different kinetic methods (both non-isothermal and isothermal methods) was found to be significantly high for sepiolite, 30B and silica-filled nanocomposites. The results were explained with the help of structure of the nanofillers, their interaction with the elastomer and the subsequent dispersion, as measured by X-ray diffraction, transmission electron microscopy and atomic force microscopy. From these analyses it was concluded that organically modified montmorillonite, sepiolite and nanosilica increase the thermal stability of the nanocomposite to a great extent due to the interaction of the reactive groups on the surface of these fillers with the polymer and high thermal stability of these inorganic fillers. Finally, degradation mechanism of HNBR in presence of the nanofillers at severe operating temperatures was investigated with the help of FTIR spectroscopy.