Fourier transform infrared spectroscopy in attenuated total reflectance geometry (FTIR-ATR), combined with a 2D correlation analysis, was here employed to investigate temperature-induced spectral changes occurring in a particular type of novel cellulosic-based nano-material prepared using 2,2,6,6-tetramethyl-piperidine-1-oxyl (TEMPO) oxidized and ultra-sonicated cellulose nano-fibers (TOUS-CNFs) as three-dimensional scaffolds, and branched polyethyleneimine (bPEI) as cross-linking agent. The aim was to highlight the complex sequential events involving the different functional groups of the polymeric network, as well as to gain insight into the interplay between the amount of bPEI and the resulting sponge-like material, upon increasing temperature. In this framework, synchronous and asynchronous 2D spectra were computed and analyzed in three wavenumber regions (900–1200 cm−1, 1500–1700 cm−1 and 2680–3780 cm−1), where specific vibrational modes of the cellulosic structure fall, and over a T-range between 250 K and 340 K. A step-by-step evolution of the different arrangements of the polymer functional groups was proposed, with particular regard to how the cooperativity degree of inter- and intramolecular hydrogen bonds (HBs) changes upon heating. Information acquired can be useful, in principle, in order to develop a next-generation, T-sensitive novel material to be used for water remediation applications or for drug-delivery nano-vectors.