The thermal diffusivity, $\alpha \rm[m^2 \cdot s^{-1}]$, is related with thermal conductivity, $\lambda \rm{[W \cdot m^{-1} \cdot K^{-1}]}$ throught the following equation:
\(\alpha = \frac{\lambda}{\rho c_p},\) where $\rho \rm{[kg \cdot m^{-3}]}$, $c_p \rm{[J \cdot kg^{-1} \cdot K]}$ are density and specific heat, respectively.
It has been widely accepted that the thermal conductivity of proteins is about one-third to one-half of that of water, $\lambda_{water} = 0.6 \rm{[W \cdot m^{-1} \cdot K^{-1} ]}$ at room temperature.
Reported molecular-weight-independent average mass density of proteins are 1.22 - 1.43 $\rm{[g \cdot cm^{-3}]}$. Fischer et al. Prot. Sci. (2004) Thus, a rough estimate of protein mass density would be about 1.35 $\rm{[g \cdot cm^{-3}]}$. By taking a close look at a protein interior, Leitner and coworkers discussed the fractal nature of protein mass density.
The density of water is 1.0 $[\rm{g \cdot cm^3}]$.
Reported specific heat of proteins are 0.30 - 0.50 $\rm{[cal \cdot g^{-1} \cdot deg^{-1}]}$. Gekko and Noguchi, J. Phys. Chem. (1979)
The specific heat of water is 1.0 $\rm{[cal \cdot g^{-1} \cdot deg^{-1}]}$.
Reported protein thermal diffusivity values at room temperature are 14.6 $\rm{[\AA^2 \cdot ps^{-1}]}$, 21.1 $\rm{[\AA^2 \cdot ps^{-1}]}$ for GFP, Mb, respectively. Yu and Leitner, J. Chem. Phys. (2005)
Buchenberg, Leitner, and Stock examined local heat diffusion coefficient, $D$, of hp36. As a result, the values of $D$ were $1.25, 1.1 \times 10^{-4}, 3.6 \times 10^{-7} \rm{[nm^2 \cdot ps^{-1}]}$ for backbone, polar, and nonpolar tertiary contact, respectively, at $T$ = 100 K. Note that these values are proportional to the temperature.
The reported value of thermal diffusivity of water is $0.1463 \times 10^{-6} \rm{[m^2 \cdot s^{-1}]}$ at $T$ = 300 K.
As a result of combined effor of experiment and theory, the energy transfer along the polypeptide chain was fund to be well described by a 1D diffusion process with a heat diffusivity of 10 $\rm{[\AA^2 \cdot ps^{-1}]}$ as contrasted to the experimental value of 2 $\rm{[\AA^2 \cdot ps^{-1}]}$. Botan et al. PNAS (2007)
The room temperature thermal diffusivity of water is 0.6 / J(=4.1855) $\times 10^{-6} \rm{[m^2 \cdot s^{-1}]}$ = 0.143 $\times 10^{-6} \rm{[m^2 \cdot s^{-1}]}$.
Note that the propagation rates, $k_p$, are related the heat diffusivity, $\alpha$, via the relation $\alpha = k_p (\Delta x)^2$.
Gerhard Stock and coworkers reported that transfer over a hydrogen bond shortcut in a beta-hairpin is about as efficient as transport over a stretch of 3-4 amino acids in the backbone Nature Communications (2021). Typical backbone tranfer times between adjacent residues are 0.2-0.3 ps, while typical contact transfer times are 2-10 ps Borau et al. J. Chem. Phys. (2020).