= Solution
If the ideal-chain segment count and segment length remain fixed, the <entropic spring> constant is proportional to absolute <temperature>. Therefore
$$
\boxed{k(60^\circ\mathrm C)=k(25^\circ\mathrm C)\frac{333.15}{298.15}
\simeq2.464\times10^{-3}\,\mathrm{N\,m^{-1}}
=2.464\,\mathrm{pN\,nm^{-1}}.}
$$
This is an increase by about $11.7\%$. The factor $k_BT$ multiplies the <free energy> penalty for the loss of chain configurations; a larger <force> is required to impose the same normalized weak extension at higher <temperature>.
Not degrading does not guarantee that a real <protein>'s folded state, effective <spring constant> or <solvent> interactions remain unchanged. Thermal unfolding and changes in <persistence length> can occur without covalent degradation. Those changes modify the experimental curve and may invalidate a fixed-$N,b$ comparison. The boxed value is the explicit ideal-<FJC> prediction under fixed segment geometry, not an unconditional thermal-<stability> prediction for the <protein>.
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