1. For a gas in a fixed volume container, pressure is directly proportional to absolute temperature:

$P \propto T$

So,

$\frac{P_2}{P_1} = \frac{T_2}{T_1}$

2. Initial temperature is given as $27^\circ\text{C}$. Convert it to Kelvin:

$T_1 = 27 + 273 = 300\,\text{K}$

3. The pressure is to be doubled:

$P_2 = 2P_1$

Therefore,

$\frac{P_2}{P_1} = 2 = \frac{T_2}{T_1}$

So,

$T_2 = 2T_1 = 2 \times 300 = 600\,\text{K}$

4. Convert back to Celsius:

$t_2 = 600 - 273 = 327^\circ\text{C}$

5. Hence, the temperature should be raised to:

$\boxed{327^\circ\text{C}}$