Which temprature is taken in Gibbs free energy equation, of the system or the surrounding? Which temprature is taken, the temprature of the system or the temprature of the surrounding? I think it should be the temprature of the surrounding. This is because if we take the temprature of the system then change in Gibbs free energy would always be zero as then, change in enthalpy of the system would always be equal to change in entropy of the system multiplied by temprature of the system.
The Gibbs free energy is a property of a system, so you should use that system's temperature when calculating it.  The Gibbs free energy is the amount of work that could be extracted from the system in a isothermal, isobaric process: i.e. the temperature and pressure of the system won't change.  Thus Gibbs energy has to do only with the temperature of the system, not of the surroundings.

There is a related but distinct variable called exergy or sometimes "availability".  This variable is given the symbol $B$, and is also a thermodynamic state function.  It is defined as $\Delta B = \Delta H - T_0 \Delta S$, where $T_0$ is the temperature of the surroundings.

Exergy represents the maximum amount of work that could be extracted from a system when that system is brought into thermal equilibrium with the surroundings, for example using Carnot engines.  Thus exergy indicates work obtainable through a combined (a) isothermal change in Gibbs free energy at temperature $T \neq T_0$ and (b) a temperature change occurs when Carnot engines are used to transfer heat from the system at $T$ to the surroundings at $T_0$ until thermal equilibrium is obtained.