Narrative:

At cruise FL410 the first officer and I noticed the cockpit temperature was high. We attempted to adjust the temperature; but even with full-cold selected the temperature continued to rise. We ran the QRH procedure 'cabin temp inop' with no effect. The QRH directed us to perform the 'cabin temperature hot' procedure. We made it to step 12 where the left pack was selected on and the right pack selected off then wait one minute. After roughly 10 seconds the left pack failed with an inoperative light illuminated. With no packs operating the cabin altitude began to rapidly climb so we selected the right pack to on. The pack off light remained illuminated so we initiated a descent initially to 25;000 ft. During the descent the cabin altitude alarm went off so the first officer and I donned our oxygen masks and performed the 'cabin altitude' procedure. The right pack did appear to come back online but even with the rapid descent it was unable to reverse the loss of cabin pressure. We requested descent to 10;000 ft. Even passing 20;000 ft. The cabin altitude showed a climb so we determined the aircraft was not capable of maintaining pressurization. We [advised ATC] and requested immediate diversion to ZZZ. Upon leveling off at 10;000 ft. The cabin altitude stabilized and we continued to an uneventful approach and landing at ZZZ.the inability of the air conditioning system to maintain cabin temperature followed by pack failure led to loss of cabin pressurization.I believe this was a critical system component failure which tends to be rare at this company. I do not feel there is an underlying deficiency or problem that needs to be addressed.

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Original NASA ASRS Text

Title: Captain reported that a pack failure resulted in a loss of pressurization and caused a diversion.

Narrative: At cruise FL410 the First Officer and I noticed the cockpit temperature was high. We attempted to adjust the temperature; but even with full-cold selected the temperature continued to rise. We ran the QRH procedure 'Cabin Temp Inop' with no effect. The QRH directed us to perform the 'Cabin Temperature Hot' procedure. We made it to step 12 where the left pack was selected ON and the right pack selected OFF then wait one minute. After roughly 10 seconds the left pack failed with an INOP light illuminated. With no packs operating the cabin altitude began to rapidly climb so we selected the right pack to ON. The PACK OFF light remained illuminated so we initiated a descent initially to 25;000 ft. During the descent the Cabin Altitude alarm went off so the First Officer and I donned our oxygen masks and performed the 'CABIN ALTITUDE' procedure. The right pack did appear to come back online but even with the rapid descent it was unable to reverse the loss of cabin pressure. We requested descent to 10;000 ft. Even passing 20;000 ft. the cabin altitude showed a climb so we determined the aircraft was not capable of maintaining pressurization. We [advised ATC] and requested immediate diversion to ZZZ. Upon leveling off at 10;000 ft. the cabin altitude stabilized and we continued to an uneventful approach and landing at ZZZ.The inability of the air conditioning system to maintain cabin temperature followed by pack failure led to loss of cabin pressurization.I believe this was a critical system component failure which tends to be rare at this company. I do not feel there is an underlying deficiency or problem that needs to be addressed.

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.