Two bodies at different temperatures T1 and T2, if brought in thermal contact do not necessarily settle to the mean temperature (T1+T2)/2?

No, thats necessarily not important to settle them at mean temperatures. Lets first see the mathematical expression for what happens when two bodies with different temperatures r in contact.

When they r brought in contact a heat current will establish between both the bodies which will contiue to flo until the temperature of both the bodies  r equal . 

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

So , Heres ur answer.

If two bodies of equal specific heat capacities and  masses  are brought in contact then they setle at equal temperature of (T1+T2)/2