$P-2 P_{0}=\frac{2 P_{0}-P_{0}}{V_{0}-2 V_{0}}\left(V-V_{0}\right)$

So, $P=3 P_{0}-\frac{P_{0}}{V_{0}} V$ as $P V=n R T$

$\Rightarrow\left(3 P_{0}-\frac{P_{0}}{V_{0}} \cdot V\right) V=n R T$

For maximum temperature $\frac{d T}{d V}=0$ $\Rightarrow \frac{d T}{d V}=3 P_{0}-\frac{2 P_{0}}{V_{0}} V=0 \Rightarrow V=\frac{3}{2} V_{0}$

Also $P=\frac{3}{2} P_{0}$

So, $T=\frac{P V}{n R}=\frac{1}{n R} \times \frac{3}{2} P_{0} \times \frac{3}{2} V_{0}=\frac{9 P_{0} V_{0}}{4 n R}$