How to find the temperature relationship between the isotherms in a compressibility factor (Z) vs pressure graph?
The compression factor $Z$ is defined as the ratio of the real molar volume with respect to the theoretical ideal

$$Z = \frac{V_m}{V_m^{ideal}}$$

where if $Z$ = 1, the gas behaves ideally. 

If we want to get some sort of understanding for how this function behaves when you change the Pressures and Temperatures of your system, we need to substitute into this equation our variables of interest. To take the simplest approach, lets just use the ideal gas law as a substitute for $V_m$ (from a quantitative sense this doesn't make sense to do but qualitatively we can still derive some relationships therefrom)
$$Z = \frac{RTP^{-1}}{V_m^{ideal}}$$
What this shows us is that $Z \propto T$. Thus, an increase in $T$ demonstrates an increase in $Z$, which is the qualitative understanding we're looking for herein.

To note, using a more realistic model for $V_m$ gets complicated; for example if you wanted to use the Van der Waals equation
$$P = \frac{RT}{V_m-b} - \frac{a}{V_m^2}$$
instead of the ideal gas equation, the $V_m$ term doesn't reduce too nicely because of that $\frac{a}{V_m^2}$ term. Gets even worse for the Virial equations.