ML/NJ
Over the Med, it’s not unusual for the to be delays in raising the next controller when flying to North Africa, I’m told. There are also conflicting reports on whether the pilot did successfully raise the over-water controller.
That said, the ACARS system time stamps those messages at 0026 to 0029 Zulu. The radios (or critical parts thereof) are in the avionics bay that was being eaten by fire when ACARS went off the air. The transponder went off the air at 0033Z, probably when its control module was destroyed by fire. Since the A320 is set up to be dynamically stable, even with the computers out, it could keep flying straight and level for a while until outside forces (wind, etc) upset it. Which apparently happened at 0037Z.
Something else people seem to be missing is that this is a fully computerized, fly-by-wire plane. It carries a backup battery pack (which I’m pretty sure is under the cockpit in a late-mark A320) to maintain power to the flight controls and computers if both engines fail and their power goes offline. There have been a rash of those battery packs going on fire in airplanes lately. The Boeing 787 has had the most high profile incidents of late:
https://en.wikipedia.org/wiki/Boeing_787_Dreamliner_battery_problems