The root mean square speed ($v_{rms}$) is directly proportional to the square root of the absolute temperature ($v_{rms} \propto \sqrt{T}$).

1. Initial State: $T_1 = -50^\circ\text{C} = 273 - 50 = 223 \text{ K}$. Let the initial speed be $v_1 = v$.

2. Final State: The speed is increased by 3 times. This means the final speed $v_2 = v + 3v = 4v$.

3. Calculation: Using the relation $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$: $\frac{4v}{v} = \sqrt{\frac{T_2}{223}}$ $4 = \sqrt{\frac{T_2}{223}}$ Squaring both sides: $16 = \frac{T_2}{223}$ $T_2 = 16 \times 223 = 3568 \text{ K}$

4. Conversion: Convert the final temperature back to Celsius: $T_2 (\text{in } ^\circ\text{C}) = 3568 - 273 = 3295^\circ\text{C}$.