Air carrier pilot reported a loss of airspeed and control of aircraft during cruise due to a non-standard temperature divergence. Flight crew descended to lower altitude and regained control of aircraft.

Narrative

Non standard temperature divergence - stick shaker activation Climbing Out of UVF FLT Company X ABCD was dispatched and assigned FL380 as the cruising FL. Cost Index was 7. During climb I checked the VNAV page displaying OPT FL370 / MAX FL384. Selected to remain at FL360 as final and arranged that with ATC. After CRUISE CHECKLIST was complete we encountered thin clouds and humidity and we started facing light turbulence. Controlling ATC was San Juan; Puerto Ricco; position 20NM SW of GEECE WPT. Reports ahead were stating continuous turbulence with potential moderate intensity. I selected Seat Belts ON; called the Flight Attendants and ordered 'moderate turbulence procedures' and selected Mach 0.76 for optimum turbulance penetration out of precaution. Weather radar was ON; manual selection WXR - 1 and WXR - 0 not depicting any hit backs of weather cells; not painting even green. ENG ANTIICE was OFF due to SAT being less than -40C. I was monitoring the PROG 2/4 and realized that the ISA Deviation started increasing. Predicting that the ENGINES will soon not be able to support the assigned FL I asked the FO to call San Juan ATC for lower. ATC did not respond initially due to multicasting. Airspeed fluctuations started accruing and we observed a rapid / sudden increase of the SAT towards -42C which gave an ISA+14C. Page PROG 2/4 displayed -42C/+14. The Airspeed started decaying and since the autothrottles were not correcting I manually selected MAX POWER by advancing the throttles towards the upper limit. The airspeed decay did not stop. At that point I ordered the FO to call a second time for descent. The rapid performance decrease related to the cone of non-standard temperature divergence activated momentarily the stick shaker. I called 'MY ACFT - A/P OFF' and disconnected the auto pilot to manually fly the ACFT and descend out of the imminent upset. As soon as auto pilot was disconnected the stick shaker seased while I applied unload at the controls. At that exact point and before exercising emergency Captains authority the ATC grant us descend to FL340 that assisted the unloading motion of the ACFT and got us to a lower altitude. During the descend the non-standard temperature divergence phenomenon was still active; resulting at a maximum of ISA +16 at FL340 without though further creating any rapid airspeed fluctuations. There were no altitude deviations prior to and no altitude violations during the incident. Emergency was not requested; since the event coincided with the clearance to descent lower after two consecutive requests to the ATC. After leveling off at FL340 we proceeded with the standardized radio report of the Non Standard Temperature Divergence point and conditions; which was accepted by the ATC. No sudden aircraft movements or rocking motions were observed; wing tips were not activated; no pre-stall flutter observed; descent was smooth and no cabin crew or passengers noticed the change of altitude or attitude. Cause:Non standard temperature divergence Phenomenon due to relatively high temperatures in the West Indies / Caribbean Area for this time of the year. Non associated with storm wx activity. Mitigation strategies such as monitoring PROG 2/4 during climb and introduction of the Non Standard Temperature Divergence Phenomenon Training at the Recurrent Training Syllabus.