Narrative:

Departed ZZZZ and climbed normally through FL250. At approximately FL250; first officer and I both noticed egt & amp; N3 on right engine indications in the yellow band. We asked ATC to stop climb at FL260 and leveled off. I pulled back right throttle and turned off auto throttles and observed both egt and N3 decrease below yellow band. I then increased power back to climb thrust; to see if it was a momentary problem; and observed both go back into yellow. Pulled right throttle back again to bring both below yellow band. I then had first officer run the engine overheat QRH and we turned off right bleed and pack. We attempted to increase power to climb thrust again to see if problem was still there and egt & amp; N3 increased into yellow band again. Reduced to below yellow band again. Handed aircraft control and ATC radios to first officer and called dispatch and [maintenance control] on satphone. [Maintenance control] thought maybe it was an internal bleed problem and didn't recommend a course of action and said it was up to us whether or not to continue. Dispatch; myself; and first officer thought the safest course of action was to return to ZZZZ for an overweight landing rather than continuing into oceanic airspace with a malfunctioning engine. We decided to [advised ATC] because of the overweight landing and also to mitigate the chance of having to go around and go to a high thrust setting again; because that is the only area where we were having problems with the engine; and we felt it was best to avoid that regime of operation if we could. We decided not to shut down the engine because it operated below the yellow limits in anything but a high thrust setting. At that time we informed ATC that we wished to return to ZZZZ and got vectors back to the ILS. Once we had the aircraft turned around; I informed the flight attendants to suspend their service and that we were returning; and then I informed the passengers over the public address system. I had the first officer go through the diversion guide in the [flight operation manual quick reference guide] to make sure we have covered everything. We also ran the overweight landing checklist in the QRH. We slowed the plane down to 250 kts in order to complete all the tasks that we had to complete before landing. The descent; approach; and landing in ZZZZ were uneventful. After landing we taxied to a hard stand and shut the engines down. Local maintenance contractors came aboard and verified that the right engine indications were very abnormal. They believed that it was actually a fuel control unit problem.

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Original NASA ASRS Text

Title: B757 Captain reported observing a high EGT reading on the right engine.

Narrative: Departed ZZZZ and climbed normally through FL250. At approximately FL250; First Officer and I both noticed EGT & amp; N3 on right Engine indications in the yellow band. We asked ATC to stop climb at FL260 and leveled off. I pulled back right throttle and turned off auto throttles and observed both EGT and N3 decrease below yellow band. I then increased power back to climb thrust; to see if it was a momentary problem; and observed both go back into yellow. Pulled right throttle back again to bring both below yellow band. I then had First Officer run the engine overheat QRH and we turned off right bleed and pack. We attempted to increase power to climb thrust again to see if problem was still there and EGT & amp; N3 increased into yellow band again. Reduced to below yellow band again. Handed aircraft control and ATC radios to First Officer and called Dispatch and [Maintenance Control] on Satphone. [Maintenance Control] thought maybe it was an internal bleed problem and didn't recommend a course of action and said it was up to us whether or not to continue. Dispatch; myself; and First Officer thought the safest course of action was to return to ZZZZ for an overweight landing rather than continuing into oceanic airspace with a malfunctioning engine. We decided to [advised ATC] because of the overweight landing and also to mitigate the chance of having to go around and go to a high thrust setting again; because that is the only area where we were having problems with the engine; and we felt it was best to avoid that regime of operation if we could. We decided not to shut down the engine because it operated below the yellow limits in anything but a high thrust setting. At that time we informed ATC that we wished to return to ZZZZ and got vectors back to the ILS. Once we had the aircraft turned around; I informed the flight attendants to suspend their service and that we were returning; and then I informed the passengers over the public address system. I had the First Officer go through the diversion guide in the [Flight Operation Manual Quick Reference Guide] to make sure we have covered everything. We also ran the overweight landing checklist in the QRH. We slowed the plane down to 250 kts in order to complete all the tasks that we had to complete before landing. The descent; approach; and landing in ZZZZ were uneventful. After landing we taxied to a hard stand and shut the engines down. Local maintenance contractors came aboard and verified that the right engine indications were very abnormal. They believed that it was actually a fuel control unit problem.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.