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...)