Yes it does. ΔG° = ΔH° - TΔS°. To a first approximation, ΔH° and ΔS° may usually be treated as constant with temperature, over a not-too-wide temperature range, but ΔG° definitely changes. In an expression like ΔG° = -RTlnK_{eq}, the ° sign means standard conditions *at the temperature T*, whatever that is.

It is worth noting that if lnK = -ΔG°/RT = -ΔH°/RT + ΔS°/R, then

d(lnK)/dT = ΔH°/RT^{2}

so the variation of K with T depends on ΔH°, not ΔS°.