Heat can only be produced, when AC current is in phase with AC voltage, like it can be seen with an ohmic resistance. But with a cap, AC current and AC voltage are phase shifted against each other by 90°.

Remember, that for an ideal cap

C = Q / U = (dQ/dt) / (dU/dt) = I / (dU/dt)

This yields

I = C x (dU/dt)

So, when

U = Uo x sin (w x t)

then

I = C x (dU/dt) = w x C x Uo x cos (w x t) = Io x cos (w x t)

Means, I and U are phase shifted by 90°.

AC impedance of cap is

Xc = Uo / Io = Uo / (w x C x Uo) = 1 / (w x C).

Or by other words: A cap stores charge in the one half phase and gives it back in the other half phase. The cap consumes "blind power", but doesn't produce heat power.

Kai