We investigate using transient non-equilibrum molecular dynamics simulation the temperature relaxation process of three structurally different proteins in water, namely; myoglobin, green fluorescence protein (GFP) and two conformations of the Ca~(2+)-ATPase protein. By modeling the temperature relaxation process using the solution of the heat diffusion equation we compute the thermal conductivity and thermal diffusivity of the proteins, as well as the thermal conductance of the protein-water interface. Our results indicate that the temperature relaxation of the protein can be described using a macroscopic approach. The protein-water interface has a thermal conductance of the order of 100-270 MW K~(-1) m~(-2), characteristic of water-hydrophilic interfaces. The thermal conductivity of the proteins is of the order of 0.1-0.2 W K~(-1) m~(-1) as compared with ≈ 0.6 W K~(-1) m~(-1) for water, suggesting that these proteins can develop temperature gradients within the biomolecular structures that are larger than those of aqueous solutions. We find that the thermal diffusivity of the transmembrane protein, Ca~(2+)-ATPase is about three times larger than that of myoglobin or GFP. Our simulation shows that the Kapitza length of these structurally different proteins is of the order of 1 nm, showing that the protein-water interface should play a major role in defining the thermal relaxation of biomolecules.
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