Let the initial pressure be $P_{1}$ and initial temperature be $T_{1}$.

Thus final pressure $P_{2}=1.004 P_{1}$ and final temperature $T_{2}=T_{1}+1$.

Using $\frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}}$

So, $\frac{ P _{1}}{ T _{1}}=\frac{1.004 P _{1}}{ T _{1}+1}$

Or $T _{1}+1=1.004 T _{1}$

Or $0.004 T _{1}=1$

$\Rightarrow T _{1}=250  \; K$