In the Nernst equation, does T refer to the temperature of the standard cell or the cell under non-standard conditions?
The Nernst equation is $\displaystyle E=E^\text{o}-\frac{RT}{nF}\ln(Q)$ where $Q$ is the ratio of activities, $a$, of products over reactants, e.g. for $aA+B\leftrightharpoons cC+D$ then $\displaystyle Q=\frac{a^c_Ca_D}{a^a_Aa_B}$. The emf of the cell is $E^\text{o}$ which is measured when the emf of the cell is zero, $E=0$, no current flows, and means that the reactants and products are at equilibrium. In this case $\displaystyle E^\text{o} =\frac{RT}{nF}\ln(K_e)$ where $K_e$ is the equilibrium constant. 

The measured emf $E$ changes with temperature as indicated by the Nernst equation and this is a good way to measure thermodynamic properties; for example the reaction free energy is  $\Delta G = -nFE$ and because $\partial\Delta G/\partial T|_p=-\Delta S$ then $\displaystyle \Delta S = \frac{\partial E}{\partial T}\bigg|_p nF$ which is a convenient way to determine the entropy change in a reaction by measuring the reaction emf at two temperatures and letting the derivative be $\Delta E/\Delta T$, which will be accurate for a small change in temperature, and give $\Delta S$ at the mean of the two temperatures. Since $\Delta G = \Delta H -T\Delta S$ the change in enthalpy can also be calculated.