## 3 Materials and Methods  
The THz/Far-IR Beamline at the Australian Synchrotron, Melbourne, Australia, was used for the experiments. The Beamline was equipped with an attenuated total reflection (ATR) apparatus, a Bruker IFS 125/HR Fourier Transform spectrometer (Bremen, Germany), an Si Bolometer and a diamond prism stage (\(n=2.40\)), and a 45\({}^{\circ}\) incoming beam angle. OPUS 8.0 software (Bruker Optik GmbH, Ettlingen, Germany) was used for the initial data analysis. Air humidity was not more than 50%. The viability of monitoring temperature related changes with the ATR apparatus, both in \"true\" ATR mode and in partial reflection-partial transmission mode, was explored with samples with bio-medical relevance. The materials were chosen for their different hydration levels, to offer varying insights into the possible temperature related changes. The temperature dependent variation of absorbance of air, water, ice, porcine rendered lard, and Lurpak(r) (unsalted) butter was explored. Lurpak(r) butter is homogeneous, and has water, lipid and protein components. It has an additional advantage of having established dielectric properties in the THz range [24]. The samples were applied through a spacer to define 2 mm thickness (water, lard, butter). At 2 mm, the path length of any returning signal from samples with absorption coefficients of \(>\)20 cm\({}^{-1}\) become negligible. A mirrored cooling bath was placed on top of the sample and fixed by a standard ATR mounting clip onto the ATR diamond prism window. In partial reflection-partial transmission mode, with a path length of \(>\)4 mm (2 \(\times\) 2 mm sample thickness), any reflected signal from the mirror returning through the samples with absorption coefficients of \(>\)10 cm\({}^{-1}\) becomes negligible. Similarly, in \"true\" ATR mode, lard and Lurpak(r) butter have an \(n\sim\) 1.5 to 1.6 in the 0.9 to 1.0 THz spectral window [24; 25], which would, under ideal attenuated total refection circumstances of a negligible \(\alpha\), deliver a \(d_{p}\) of \(<\)0.01 mm. Thus, any interference from the mirror reflection back through the sample is similarly negligible. Polarisation of synchrotron radiation is a combination of linear (along the extraction mirror slit) and circular polarisations [26]. These two components arise due to the bending magnet caused dipole-emission inside the magnet and the edge-emission at the entrance/exit of the magnet edge. The THz and IR microscopy beamlines share the synchrotron radiation extracted from the magnet. The THz/Far-IR beamline receives a larger portion of the edge-emission compared to the dipole-emission. Polarisation is defined in the plane of incidence as Es and Ep, which are perpendicular (\(\perp\)) and parallel (k) to the plane (or TE and TM modes), respectively. The reflected radiation at the 45\({}^{\circ}\) incidence usually does not experience phase change upon reflection at the sample-prism interface for low refractive index (\(n_{2}<1.6\)) samples, which is typical for low \"bulk water\" biological samples. However, the P-polarised (TM; Ez) radiation, which probes the absorbance in the direction perpendicular to the prism-sample interface, has a strong dependence of the reflected phase on \(n_{2}\). At \(\theta i=45^{\circ}\) incidence, a phase change of \(\pi\) occurs when \(\theta_{B}<\theta_{i}<\theta c\) (\(\theta_{B}\) and \(\theta c\) are the Brewster and critical angle, respectively) and the reflected Ez component becomes Ey. The consequence of the phase dependence of the TM mode makes polarisation analysis of ATR signals complicated, and most of the published data do not discriminate polarisation. This approach was adopted in the current study. Future experiments will include a defined incident polarisation combined with polarisation analysis at the exit after the sample. The ATR unit had a Thermal Stage fitted, with a capability to control the temperature of the sample and the crystal.