In case of TT-OSL the electron can be transfered to any trap by heating and then those traps will also give OSL. While in case of TAOSL the temperature assists the electron within the same trap and OSL come from that trap only.
You might try Professor Vasilis Pagonis' website at McDaniel College (in Westminster, Maryland, USA). He has been studying the physics of both TT-OSL and TA-OSL for the past 5 or 6 years and is really the most knowledgeable person on this subject that I know. Professor Pagonis has very helpfully put the most important 73 his 100's of publications in an abstract form on his personal webpage.
http://blog.mcdaniel.edu/vasilispagonis/
Here is abstract #72 Modeling TL-like thermally assisted optically stimulated luminescence (TA-OSL) and abstract #32 A theoretical model for a new dating protocol for quartz based on thermally transferred OSL (TT-OSL). Links to the publications are just below the abstract and can be downloaded for free.