TSDC spectra of Myoglobin (Mb) and human Hemoglobin (Hb) have provided a large deal of information about the properties and role played by water molecules organized in the structure of both proteins at very low hydration degree delta (delta=0.01 divided by 0.62). In particular, complementary TSDC and optical absorption spectroscopies applied to Mb have put in evidence a critical hydration level which induces a partially irreversible structural change. TSDC analysis of Hb has supplied information about the hydration network, particularly with regard to the average number of hydrogen bonds established by the water molecules in the inner cages of the polymer at different hydration degrees.