What I've seen is a construction of a quasi-inverse for RHom(T,-), defined as $-\otimes_A^L T$, as you wrote. This last symbol should be interpreted as follows. Given a left A-module M, we define a presheaf which with each U associates $M\otimes^L_A T(U)$. Finally $M\otimes^L_A T$ is defined as the sheafification of the former.
I should have a reference for this, let me check.