Two Line Mechanics report they were informed by Quality Assurance that a hot section overtemp inspection on a B727-200 APU was required; but had not been accomplished; prior to their signing-off a pilot write-up for an APU hot start.

Narrative

Myself my work partner received a B727-200 aircraft at around XA:30am. The below pilot discrepancy was one of three on arrival. Log page: APU hot start; fire handle pulled; complied with QRH; temperature rose to 750 degrees C (Celsius). Reset fire handle; started APU and noticed EGT rising and APU slow to spool; aborted start. Waited 10 minutes and started again. APU started normal and ran for 10 minutes; no defects noted; referenced Jet Run-up Handbook (JRH). Me and Mechanic X observed and duplicated no-start; and no-spool of the APU. Therefore; we continued in our troubleshooting of the APU system. We believe the APU was extremely cold-soaked; after completing a 3.5 hour flight and landing here in ZZZ in 9 degree F weather; plus the wind chill.We attempted a start of the APU; and duplicated the no-start and no-spool scenario. After a required APU starter duty cool down period; we attempted a 2nd start; which was a normal start. Indications were normal as well; confirming our belief that the APU was extremely cold-soaked. The crew came out to the aircraft approximately 1.5 hours later; after we had run the APU and signed it off. They started the APU and had a normal start; and departed.Upon arrival at ZZZ1; the Quality Assurance department felt that since the write-up stated that the APU had a hot start and indicated 750 degrees C; it required an overtemp inspection. They deferred (MEL) the APU at the station (ZZZ1) until an overtemp inspection could be complied with. One week later the aircraft went into B-Check; where a boroscope and detailed inspection of the APU was performed. They determined the APU showed signs of coking and Quality Assurance made the decision to change the component. The APU had been installed for approximately 700 hours with some related history.I believe at the time I dispatched the aircraft; that there was no-spool and no-start of the APU; so I did not believe any further action was required. The JRH disagrees with me and states that when an indication of more than 710 degrees C is indicated; it requires an overtemp inspection. I did not comply with this required inspection and should have; even though I believed the discrepancy to be some kind of indication problem or possible circuitry problem due to the extreme cold. Company management has brought to my attention that this inspection is required no matter what; per the company JRH. This action will be followed to the letter from this point forward.