An assumption. "They knew it wouldn't work". Have a think. You were told that it had overheating issues on the ground, but that it would work in flight. It's actually a tad difficult for them to test that particular scenario, unless you're suggesting they take the aircraft out for a flight to have a look. Nevertheless, there is a real failure sequence that leads to exactly this outcome. You may not believe it, but then you have no technical knowledge of the aircraft
Really. You're trying to tell me this. IFE per se might not be on the MEL, as it is not an airworthiness item. But, the systems that run it certainly are.
ECAM:
VENT IFE BAY VENT FAULT
IFEC - OFF
When, the IFEC pb-sw is set to OFF:
IFE BAY VENT AVAIL IN FLT
MEL:
On ground with both packs running and the CAB FANS pb-sw set to ON:
Set the IFEC pb-sw to Auto and wait for 5 min.
The alert appears with the INFO message IFE BAY VENT AVAIL IN FLT on the STATUS SD page:
Set the IFEC pb-sw to OFF on ground.
The IFE bay ventilation is insufficient on ground due to high ambient temperature. The IFE bay ventilation available in flight.
So, there you go. An MEL.