Narrative:

During a routine single engine training flight; the left engine would not restart in flight. Starter would not turn the engine at all. The right engine was hot and approaching max cht (cylinder head temperature). An engine-cooling descent was started after the decision was made to discontinue starting and return to [departure airport] single engine because maintaining altitude on only the right engine would result in possible right engine overheating. The position was 7;000 feet; 14 NM [from departure airport]. [Pilot receiving instruction] continued flying and instructor conducted checklists and coordinated with ATC. ATC contact was made at 4;000 feet and crew requested direct to the numbers rnwy 9L. Instructor pilot conducted single engine landing.

Google
 

Original NASA ASRS Text

Title: An instructor pilot reported being unable to restart the left engine in a PA-44 after conducting single engine training with a student. A successful single engine approach and landing was made.

Narrative: During a routine single engine training flight; the Left engine would not restart in flight. Starter would not turn the engine at all. The right engine was hot and approaching max CHT (Cylinder Head Temperature). An engine-cooling descent was started after the decision was made to discontinue starting and return to [departure airport] single engine because maintaining altitude on only the Right engine would result in possible Right engine overheating. The position was 7;000 feet; 14 NM [from departure airport]. [Pilot receiving instruction] continued flying and instructor conducted checklists and coordinated with ATC. ATC contact was made at 4;000 feet and crew requested direct to the numbers RNWY 9L. Instructor pilot conducted single engine landing.

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.