Answer
a) $2^2$
b) Remains constant.
Work Step by Step
a) We know that
$$v_{\rm rms}=\sqrt{\dfrac{3k_BT}{m}}$$
$$v_{\rm rms}^2= \dfrac{3k_BT}{m} $$
So increasing the RMS speed by a factor of 2 increases the temperature by a factor of $2^2=4$ since $T\propto v_{\rm rms}^2$
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b) We know that the molar specific heat at constant volume of a gas $C_{\rm V}$ depends only on the element of the gas, not the heat, the pressure, or the temperature of the gas. And not also the volume.
So, $C_{\rm V}$ would not change by increasing the RMS speed by a factor of 2 or by any factor.
