A CRJ with an APU deferred "within the manual limitations" can easily reach 100+ degrees in the cabin with an OAT of 60. Have fun with that. And as for the bold part, well I just don't know what to say about that kind of logic...
If you deferred an inop APU at Piedmont you'd never fly, and they'd find some way to fire you quickly.
CRJ inop APU = Dash 8 with operating APU.