Consider a system X that is neither in thermal equilibrium with...

Let $T_X$, $T_Y$, and $T_Z$ be the temperatures of systems $X$, $Y$, and $Z$ respectively.

Since system $X$ is not in thermal equilibrium with system $Y$, $T_X \neq T_Y$.

Since system $X$ is not in thermal equilibrium with system $Z$, $T_X \neq T_Z$.

From these two conditions, it is possible that $T_Y = T_Z$ (for example, $T_X = 10^{{}^{{}^{\circ}}}\text{C}$, $T_Y = 20^{{}^{{}^{\circ}}}\text{C}$, $T_Z = 20^{{}^{{}^{\circ}}}\text{C}$) or $T_Y \neq T_Z$ (for example, $T_X = 10^{{}^{{}^{\circ}}}\text{C}$, $T_Y = 20^{{}^{{}^{\circ}}}\text{C}$, $T_Z = 30^{{}^{{}^{\circ}}}\text{C}$).

Thus, systems $Y$ and $Z$ may or may not be in thermal equilibrium.