If it is in the trans as you suspect the resistance necessary to stall would create a good deal of heat. Is the trans area much hotter than the engine block? This is a very doubtful cause of stalling.
When it stalls does it just slowly come to a stop or does it shake a shudder a bit when stopping?
I suspect it is fuel related and a pressure gage would answer that if just a few minutes
.
Did you do any checks once stalled like spark?
Dave Neptune