One of them, I had to fly with an aircrew from Mildenhall back to Tinker AFB to pick up my airplane that was in for depot maintenance and a paint job. We had to wait a couple of days before the airplane to be released, finally cleared for the flight back home. I usually sat in the IP seat for takeoff and landings. During takeoff out of Tinker I noticed that the egt (exaust gas temperature) on one of the engines was running hot, right at the limits. The other three engines were lower, where you would normally expect them. We flew to Pease AFB where we'd depart for Mildenhall the next evening. I mentioned to my AC that the engine got hot on takeoff but was in normal range during the rest of the flight. He didn't write it up in the aircraft forms. We departed the next night, same results. We had a VIP onboard for a PAX so I gave up my seat and slept for most of the flight across the pond. Once we were on the ground and parked I told the AC about the engine again which he mentioned to maintenance at the debriefing. I was off for a couple of days, when I returned to work the pilot and copilot were there waiting for me. An aircraft returning from depot has to go through a phase inspection which is also an acceptance inspection. Jet shop did a borescope inspection on the hot section of the engine that was running hot, they found a burn can that was ready to disintegrate. The pilot handed me a letter of accommodation, told me he would never question my judgment again.