thermodynamics - Which temperature is meant in the Gibbs free energy equation?

In the equation for Gibbs free energy change, $\Delta G = \Delta H - T\Delta S$, does $T$ refer to the temperature of the system or the surroundings?

I know we have to calculate Gibbs free energy of the system but the criterion for spontaneity says $\Delta S_\mathrm{total}$ should be greater than zero. When we relate it to Gibbs free energy to show that Gibbs free energy change should be always negative, we keep both system and surrounding temperature same with pressure also constant. Then how can the process occur? Wikipedia says that it is chemical potential that undergoes changes there but what about Gibbs free energy change?

From Wikipedia:

Thus, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure: both isothermal and isobaric. Such processes don't move on a P—V diagram, such as phase change of a pure substance, which takes place at the saturation pressure and temperature. Chemical reactions, however, do undergo changes in chemical potential, which is a state function. Thus, thermodynamic processes are not confined to the two dimensional P—V diagram. There is a third dimension for n, the quantity of gas