The zeroth law of thermodynamics states that if two thermodynamic
systems are each in thermal equilibrium with a third, then they are in
thermal equilibrium with each other. Accordingly, thermal equilibrium
between systems is a transitive relation.
(if A =B and B=C, then C=A)
The fact that temperature obeys a transitive property is by no means intuitive!
If A likes B; B likes C; Does not imply that A likes C.
The city closest to city A is B, the city closest to B is C, but A is not always the closest to C
Or this popular example.
Rock > Scissors, Scissors > Paper. But Rock > Paper is definitely not true
To remind us that temperature obeys a transitive property is the reason why there exists a zeroth law of thermodynamics.