Is the Standard hydrogen electrode potential at T other than 298 K also zero?
According to the definition used by IUPAC, the standard electrode potential $E^\circ$ of the standard hydrogen electrode is zero at all temperatures.


  For solutions in protic solvents, the universal reference electrode for which, under standard conditions, the standard electrode potential ($\ce{H+}/\ce{H2}$) is zero at all temperatures.


The absolute electrode potential $E^\circ(\mathrm{abs})$, however, depends on temperature. Its value can be calculated from thermodynamic quantities (e.g. $\Delta G^\circ$). The recommended value for $T=298.15\ \mathrm K$ is $E^\circ(\mathrm{abs})=4.44(2)\ \mathrm V$.