This dataset supports the publication: "The impact of moderate heating on human bones: an infrared and neutron spectroscopy study", (M.P.M. Marques, L. Batista de Carvalho, D.M. Gonçalves, E. Cunha and S.F. Parker, (2021)). The dataset consists of eight zip files: Figure_1.zip, Figure_2.zip, Figure_3.zip, Figure_4.zip, Figure_5.zip, Figure_S2.zip and Figure_S3.zip. In each zip file is a copy of the Figure (as .jpg file) from the manuscript or the supplementary material plus the spectra used to create it. Figures 1-4 are divided into two blocks of spectra: on the left ("A" in the figure) are the spectra from samples burned aerobically and on the right ("B" in the figure) are the spectra from samples burned anaerobically. Figure S2 is similar except that "A" is the top part and "B" the lower part of the figure. For each of these, the spectra are included with the figure. Figure 5 has three blocks of spectra a comparison of aerobically and anaerobically burned bone as measured by infrared ("A", top), INS using MAPS ("B", middle) and INS using TOSCA ("C", bottom). In this case, the .zip file has three directories, each of which has the spectra for the appropriate part. Figure S3 has the figure and the TOSCA INS spectrum of cyanamide. The data files consist of two columns of ASCII: column 1 is the energy transfer in wavenumber (cm-1), column 2 is the intensity (Absorbance for the infrared data, S(Q,w) (arbitrary units) for the INS data). These may be viewed with any text reader or can be loaded into programs such as Excel or Origin to display the spectra. The data file names have the format: Fxxx_A.dat or Fxxx_An.dat, and Txxx_A.dat or Txxx_An.dat, where F or T denotes the bone is from the femur or the tibia, respectively, xxx is the burning temperature (in degrees Celsius) and A denotes burned aerobically and An denotes burned anaerobically. In addition, there are files called F_unb.dat ot T_unb.dat, which is the unburned femur or tibia respectively, HAp.dat which is the reference highly crystalline, stoichiometric hydroxyapatite purchased from NIST and Cyanamide.dat which is the TOSCA INS spectrum of cyanamide.