Narrative:

We arrived at aircraft and completed duties as normal. We noted two placards; one for one of the left engine overheat loops inoperative; and one fire loop inoperative on the same engine. Preflight; taxi; and takeoff all were normal. At approximately FL260 on climb out; and after the first officer B went back for his break; we received the left engine overheat caution message. We asked ATC for a temporary level off; which we performed; then we accomplished the engine overheat checklist up to and including retarding the throttle to idle.after discussing the situation; both the copilot and I felt this could be related to the inoperative loops and therefore a false message. All engine indications were completely normal. I decided to call maintenance control to discuss the situation before deciding whether to shut down the engine.the person we spoke to; after we described the situation; agreed that this was probably a false indication. He stated that if the egt is matching closely to the other engine; there was likely no leak; as a higher egt would indicate a higher bleed demand compensating for a leak.additionally; while we were discussing this; the overheat message extinguished. Based on the preponderance of evidence; as I saw it at the time; we opted to continue the flight. The overheat message flickered on several more times during the flight; but always extinguished shortly thereafter. This also reinforced; in my mind; the nature of the indication as a false one. We carefully monitored both air and secondary engine systems throughout the flight and we landed normally and placed the write up in the logbook.later; I discussed this with my copilot and others; and I have reevaluated this as an error on my part. It is possible; however unlikely; that the flickering could have meant a real; but intermittent problem; or even a failure of the other circuit; leaving us with only the second fire loop to indicate a serious problem. That and the nature of our route of flight; for a time being over sparse diversion options; convinced me that we should have shut the engine down and returned. I will be more conservative in my judgement on this sort of issue in the future.I relied too heavily on maintenance control's input and have since learned that the folks there; as well intentioned and competent as they may be; do not have the same level of experience and corporate knowledge they once had. Although they are a valuable source; they should be just that; a source.I should've have completed the engine shutdown when the light didn't immediately go out; though it did do so after several minutes. I think it would be helpful to have guidance on how long to wait before doing so in the engine overheat checklist. Obviously; error on the side of caution; which I will be sure to do so from now on.

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Original NASA ASRS Text

Title: B777 flight crew reported accepting an aircraft with MELs for one fire and one overheat loop on the left engine inoperative. Climbing through FL260 an overheat warning is displayed for the left engine. The crew is reluctant to shut the engine down due to the MELs; and contacts Maintenance Control; who reinforces the crew's decision to keep the engine running. Flight continues to destination.

Narrative: We arrived at aircraft and completed duties as normal. We noted two placards; one for one of the left engine overheat loops inoperative; and one fire loop inoperative on the same engine. Preflight; taxi; and takeoff all were normal. At approximately FL260 on climb out; and after the First Officer B went back for his break; we received the left engine overheat caution message. We asked ATC for a temporary level off; which we performed; then we accomplished the engine overheat checklist up to and including retarding the throttle to idle.After discussing the situation; both the copilot and I felt this could be related to the inoperative loops and therefore a false message. All engine indications were completely normal. I decided to call Maintenance Control to discuss the situation before deciding whether to shut down the engine.The person we spoke to; after we described the situation; agreed that this was probably a false indication. He stated that if the EGT is matching closely to the other engine; there was likely no leak; as a higher EGT would indicate a higher bleed demand compensating for a leak.Additionally; while we were discussing this; the overheat message extinguished. Based on the preponderance of evidence; as I saw it at the time; we opted to continue the flight. The overheat message flickered on several more times during the flight; but always extinguished shortly thereafter. This also reinforced; in my mind; the nature of the indication as a false one. We carefully monitored both air and secondary engine systems throughout the flight and we landed normally and placed the write up in the logbook.Later; I discussed this with my copilot and others; and I have reevaluated this as an error on my part. It is possible; however unlikely; that the flickering could have meant a real; but intermittent problem; or even a failure of the other circuit; leaving us with only the second fire loop to indicate a serious problem. That and the nature of our route of flight; for a time being over sparse diversion options; convinced me that we should have shut the engine down and returned. I will be more conservative in my judgement on this sort of issue in the future.I relied too heavily on Maintenance Control's input and have since learned that the folks there; as well intentioned and competent as they may be; do not have the same level of experience and corporate knowledge they once had. Although they are a valuable source; they should be just that; a source.I should've have completed the engine shutdown when the light didn't immediately go out; though it did do so after several minutes. I think it would be helpful to have guidance on how long to wait before doing so in the engine overheat checklist. Obviously; error on the side of caution; which I will be sure to do so from now on.

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.