Ok, I have an affine (normal) toric variety $X = \text{Spec} k[\sigma]$. Suppose that $F, G$ are two torus invariant Weil divisors on $X$. Is there any relatively straightforward way to compute $$ \text{Ext}^i_{\mathcal{O}_X}(\mathcal{O}_X(F), \mathcal{O}_X(G))? $$ If it helps, I'm happy to assume that $F$ and $G$ are effective (one can twist to that case up to isomorphism anyways), but obviously I can't assume that $F$ is Cartier...

I'd be particularly interested in doing this if $X$ is dimension 3. Even (and perhaps especially for) specific examples.