The first formula has the term RT/zF with T=temperature. So what's the problem?
Phase transition.
That too, but consider a reaction A (aq) + B (s) -> C (s) + D (aq), where all the reactants and products are in there standard state. Then what if T= 400 K? ln 1 = 0, so E = E0 anyway, even though the temperature is wrong.
Eo will change with temperature, so you would have to find the value of Eo at 400K.
My conclusion too, but different values of E0 are rarely provided. Is it safe to assume that E is independent of T at relatively small derivations from T = 298 K?