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Dear student,

 (a) No, thats necessarily not important to settle them at mean temperatures. 

When two bodies at different temperatures T₁ and T₂ are brought in thermal contact, heat flows from the body at the higher temperature to the body at the lower temperature till equilibrium is achieved, i.e., the temperatures of both the bodies become equal.  

Let before the bodies settle at equal temperature the heat exchange between them is Q and the temperature at thermal equilibrium is T

Then

Heat lost by body at higher temperature is Q = M₁C₁(T₁-T)

Similar amount of heat is gained by the second body so Q= M₂C₂(T-T₂)

then M₁C₁(T₁-T)= M₂C₂(T-T₂)

Then T = ( M₁C₁T_{1 +} M₂C₂T₂ ) / (M₁C₁+M₂C₂)

B) The equilibrium temperature is equal to the mean temperature (T₁ + T₂)/2 only when the thermal capacities of both the bodies are equal.

Regards