Two thoughts:
1) The obvious: Turn off A/C packs (or run them from the APU) to gain EGT margin.
2) If the aircraft is enroute back to main base, and no further hot-day, rated-thrust takeoffs are anticipated before that, it does seem reasonable to press on, so long as the engine remains more-or-less normal.
I'd think it less wise to dispatch from main base in that condition, though. The engine won't heal itself.