In discussions about large temperature rises near thunderstorms, the process has been researched and documented at the very least in the report from 1992 on VH-JJP in Western Australia:
The aircraft was on a scheduled domestic passenger service flight from Karratha to Perth at Flight Level 310 (31,000 ft). As the aircraft entered cloud while diverting around a large thunderstorm, there was a sudden and significant rise in the outside air temperature. A short time later, all four engines progressively lost power and the aircraft was unable to maintain altitude. During the next 17 minutes, numerous attempts to restore engine power were made without success until, approaching 10,000 ft altitude, normal engine operation was regained.
Appendix 1 of the report contains the Meteorological research of the warm air outflow from the top of the thunderstorm which caused the event.
The report is here:
http://www.atsb.gov.au/publications/...200286_001.pdf