The temperature of gas is $-50^{\circ }\text{C}$. To what temperature the gas should be heated so that the RMS speed is increased by $3$ times?

The RMS speed $v_{rms}$ is proportional to the square root of the absolute temperature $T$:
$$v_{rms}\propto \sqrt{T}$$
Initial temperature $T_1=-50^{\circ }\text{C}=223\text{K}$.Let the initial speed be $v_1$. The speed is increased by $3$ times, so the final speed $v_2=v_1+3v_1=4v_1$.
$$\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}⟹4=\sqrt{\frac{T_2}{223}}$$
Squaring both sides:
$$16=\frac{T_2}{223}⟹T_2=16\times 223=3568\text{K}$$
In Celsius:
$$T_2=3568-273=3295^{\circ }\text{C}$$