Heat lost in ideal capacitor charging
The problem with these theoretical examples lies in the fact the current is assumed infinite for 0 seconds. Crudely substituting this in the conservation law:

$$ \frac {\partial \rho }{\partial t} +\nabla \cdot \mathbf {J} = 0 $$

$$ \frac { \rho }{ 0 }+ \infty \neq 0 $$

Since charge is conserved, the assumption of infinite current in zero time is wrong.

How much power is dissipated \$P_{diss}=VI\$ cannot be defined, since the definition of the current is false.

So, the answer is: cannot be defined

EDIT
Note that the dissipation neither is 0&nbsp;W because R = 0 \$ \Omega\$. For the same reason as above: \$ P = I^2R = \infty^2 \cdot 0 \$, which is not defined.