This should definitely be conduction.  The energy transfers from the gas after the shock layer into the heat shield via convection.  Then the energy travels via conduction throughout the vehicle and into the payload.  This remark is also noted as citation needed.  I'm not going to add a citation, mostly because I don't feel motivated enough to look up the source, but any text book on heat transfer or reference on the science of convection and conduction heat transfer would suffice.  It's not very advanced and so is readily available.
192.12.88.2