Predict the standard potential at 310 K for the cell constructed from the hydrogen electrode and metal-insoluble salt electrode
Predict the standard potential at 310 K for the cell constructed from the hydrogen electrode and metal-insoluble salt electrode $\ce{Ag(s)|AgCl(s)|Cl−}$


The reactions would be:
$$\ce{AgCl +e- -&gt;Ag +Cl-}\tag{$E_1$ V}$$
$$\ce{2H+ +e- -&gt;H2}\tag{0 V}$$
Adding:
$$\ce{AgCl +H_2-&gt;Ag +Cl- +2H+}\tag{$E_1 V$}$$

The standard potential would be:
$$E=E^\circ -\frac{RT}{\nu F}\log\ce{\frac{[Cl- ][H+]}{P_{H2}^2}}\quad (E^\circ =E_1,\nu=1)$$
H
Now you have $E_1$, also you must have $\ce{[Cl- ],[H+ ]}$ beforehand, there's no other way, other than considering the fact that (standard) Hydrogen electrode is maintained at $\text{1M}$ and $\text{1 atm}$, and to maintain charge $\ce{[Cl- ] =[H+ ]}$.In that case, 
$$E=0.222-\frac{8.314\times 310}{96500}\ln(1)=0.222$$



Just for info (from Wikipedia):
$$\begin{array}{c|c}\text{Temperature}&amp;\text{Potential} E^\circ\\
^\circ\text{K} &amp;\text{V versus SHE at the same temperature}\\\hline
298 &amp;0.22233\\
333 &amp;0.1968\\
398 &amp;0.1330\\
423 &amp;0.1032\\
\end{array}$$
Also when you consider $\Delta S\ne\text{ constant}$:(A.J. Bard, R. Parson, J. Jordan, "Standard Potentials in Aqueous Solution", Marcel Dekker, Inc., 1985.)
$$E^\circ=0.23695 - 4.8564\times10^{−4}t - 3.4205\times10^{−6}t^2 - 5.869 \times 10^{−9}t^3$$