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.

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.

Reference Added: A. A. Beilinson. Coherent sheaves on $\mathbb{P}^n$ and problems in linear algebra. Funktsional.Anal. i Prilozhen., 12(3):68–69, 1978. (it's this one, if I remember correctly, but I might not...)