I've been thinking the same thing - if you took everything out of the inside of the G4, would the mini fit in without removing the case? But would that cause heating issues as there's then not enough air freely moving around the Mini?
Or, if you remove the case, would that then causing heating issues (as I presume it relies on air flow that is directed by the enclosure. Without the enclosure, is there a risk that not enough air is routed to where it is needed?