1. Use the pressure-temperature relation for a gas in a closed vessel

Since the vessel is closed and rigid, the volume is constant. For a fixed mass of gas at constant volume,

$P \propto T$

where $T$ is the absolute temperature in Kelvin.

So,

$\frac{\Delta P}{P} = \frac{\Delta T}{T}$

2. Given percentage increase in pressure

The pressure increases by $0.4\%$ when the temperature is raised by $1^\circ C$.

A rise of $1^\circ C$ is the same as a rise of $1\,K$, so

$\Delta T = 1\,K$

Also,

$0.4\% = \frac{0.4}{100} = 0.004$

Thus,

$\frac{\Delta P}{P} = 0.004$

3. Apply the formula

$\frac{\Delta P}{P} = \frac{\Delta T}{T}$

$0.004 = \frac{1}{T}$

So,

$T = \frac{1}{0.004} = 250\,K$

4. Final answer

The initial temperature of the gas is

$\boxed{250\,K}$