B737 First Officer reported high EGT on number 2 engine in cruise. Crew diverted and landed uneventfully.

Narrative

We were approximately 50 miles north of fix ZZZZZ at FL310; still on HF with ZZZ but we're directed to contact ZZZ1 on VHF at ZZZZZ; my Captain and I both observed the rapid accelerating EGT temperature on the number two engine; my captain; PF (Pilot flying) immediately performed the appropriate memory items for the said malfunction. We [advised ATC] through the help of other aircraft who were in closer range and had established communication with ZZZ1; we descended from FL310 to FL210 for single engine our single engine altitude; I took over the flying duties while the Captain ran the checklists; communicated to ATC; Dispatch; flight attendants; our passenger onboard and also two DH (Dead Head) pilots. After communicating with Dispatch; we came to an agreement ZZZZ would be our diversion airport. We were given priorities and direct to ZZZZ; rescue equipment were requested to standby in the event we do need it. Once all notifications were made; Captain took over flying duties as pilot flying and performed a safe landing into ZZZZ.