Does standard electrode potential depend upon temperature?

Yes, the standard reduction potential does depend on temperature. The definition of the standard reduction potential is stated in Ref.1 as:

A standard electrode potential $E^\circ$ is defines as the potential (in Volts, $\pu{V}$) of a half-reaction relative to a reference electrode at a specific temperature, all chemicals being at their standard states at unit activity. These states may be arbitrarily defined as pure crystalline solids, pure liquids, ideal gases at one atmosphere fugacity ($\pu{101325 \times 10^{5} Pa}$), and ideal solutes at unit molality. The most common temperature for the tabulation of standard electrode potentials, as for their thermodynamic data, is $\pu{25 ^\circ C}$ ($\pu{298.15 K}$).

Accordingly, tabulated data is chosen to be at $\pu{298.15 K}$ for the convenience. This is also beneficial that the most common reference electrode is the Standard Hydrogen Electrode (SHE) for the solvent water:

$$\ce{2H+_{(aq)} + 2e- <=> H2_{(g)}} \tag1$$

$E^\circ_{(\ce{H+/H2})}$ for the above half-reaction is been assigned as zero volts at all temperatures. Extended work over $\pu{298.15 K}$ by De Béthune and coworkers shown that the temperature dependence of $E^\circ$ is approximately linear between $\pu{273.15 K}$ and $\pu{373.15 K}$ according to the following equation (Ref.2-Ref.4):

$$E_T = E^\circ_{298} + (T - 298.15)\left(\frac{dE^\circ}{dT}\right)_{298} \tag2$$

References:

1. Steven G. Bratsch, “Standard Electrode Potentials and Temperature Coefficients in Water at $\pu{298.15 K}$,” Journal of Physical and Chemical Reference Data 1989, 18(1), 1-21 (https://doi.org/10.1063/1.555839).
2. A. J. De Béthune, T. S. Licht, N. Swendeman, “The Temperature Coefficients of Electrode Potentials: The Isothermal and Thermal Coefficients—The Standard Ionic Entropy of Electrochemical Transport of the Hydrogen Ion,” Journal of The Electrochemical Society 1959, 106(7), 616 (doi:10.1149/1.2427448).
3. G. R. Salvi, A. J. De Béthune, “The Temperature Coefficients of Electrode Potentials: II. The Second Isothermal Temperature Coefficient,” Journal of The Electrochemical Society 1961, 108(7), 672 (doi: 10.1149/1.2428187).
4. André Jacques De Béthune, Nancy A. Swendeman Loud, In Standard Aqueous Electrode Potentials and Temperature Coefficients at $\pu{25 ^\circ C}$; C. A. Hampel: Skokie, ILL, 1964.