Air carrier Dispatcher reported notification from a flight crew of an engine malfunction. The flight returned to the departure airport and landed overweight.

Narrative

I got an ACARS from the event flight saying that they had an engine EGT overheat that they were unable to control; they had [requested priority handling]; and they were returning to their departure airport. The flight had just taken off approximately within the past 5-10 minutes and was already turning back towards the airport. I responded that I copied their message and began going though the diversion procedures; including communications with the ATC desk; Maintenance Dispatcher; and Maintenance Control; while sending an updated release and landing data to the crew. I The flight landed overweight and had hot brakes but the emergency personnel did not find any indications of fire or engine damage. In the debrief after the flight had blocked back in; the Captain explained that they had unsuccessfully tried to call me over SATCOM prior to sending me the ACARS message notifying me of the problem. They added that when they tried the SATCOM call; they had selected domestic when dialing. It connected to the Dispatch phone tree but continued to ring; as if nobody was picking up the call and would continue to roll to other phone lines. They also mentioned international was another available dialing option; but they didn't try calling it. During this event; I don't recall seeing my phone lines or the SATCOM phone lines ringing. After the phone continued to ring for some amount of time; the Captain decided to message me instead.