I'll just give my method: (Not solving... too lazy )

Power of the source is P

Let the mass of the object be some m.

Then, in a time t, heat supplied = Pt = mC

or .

Now, change in volume of the cylinder =

Hence find change in radius.

Now, there is no external torque on the system, hence,

We can calculate the two moment of inertias using the standard result, and also using the change in volume that we deduced previously.

Using that, you get as a function of time. Differentiate it twice wrt time to get ur result :)