New information on a protein's structure, intra- and intermolecular hydrogen bonds, or metal-ligand bond properties can be unraveled in the far-infrared (far-IR)-terahertz-domain (600-3 cm(-1) or 18-0.1 THz). In this study, we compare the performances of thermal sources with synchrotron far-IR to record reaction-induced Fourier transform infrared (FT-IR) difference signals with proteins in solution. Using the model protein Cu-azurin placed in a short path length electrochemical cell adapted for transmission spectroscopy in vacuum-purged optics, we show that minute spectral shifts induced by metal isotope labeling or temperature changes are detected using the far-IR beamline AILES of the synchrotron SOLEIL. On one hand, these data allow us to identify modes involving Cu-ligand vibrations and pave the way for the analysis of metal sites or metal redox states of proteins not amenable to resonance Raman spectroscopy. On another hand, small band shifts or changes in band intensity upon temperature modifications show that far-IR difference spectroscopy allows one to extract from a complex background hydrogen-bonding signatures directly relevant to the protein function. For Cu-azurin, a temperature-sensitive IR mode involving Cu(II)-His vibrations points to the role of a hydrogen bond between a Cu histidine ligand and the water solvent in tuning the Cu(II)-histidine bond properties. Furthermore, these experimental data support the possible role of a His117-water interaction in electron-transfer activity of Cu-azurin proposed by theoretical studies.