The main source of heat will be the output devices.
The heat from them is largely conducted to the fins of the heat sink where it is dissipated by convection (and to a smaller extent by radiation).

Any radiant heat produced within the case is in turn dissipated by radiation and convection from the exterior of the case. All the sound deadening material will do is to absorb the heat which will eventually be conducted through and dissipated from the exterior of the case.