two systems in thermal contact trade energy to maximize the net entropy of the ensemble.

Actually the assumption is that two systems in thermal contact come to some equilibrium state.

Let this equilibrium state _maximize something_, call it S, and use calculus.

Energy is conserved.

Therefore the energy change in on system equals minus the energy change in the other, and the change in S wrt the energy change in each system has to be equal in both systems at the maximum of total S.

Call that change wrt energy the (inverse) temperature. Two systems in thermal contact come to the same temperature, is then what the assumption of some equilibrium of something comes to, after you rename the derivatives.

Only the assumption of an equilibrium has been introduced to get this.

That's where