The angle subtended is given by the arc length divided by the radius:

$$\phi = \frac{L_2}{R+t/2}=\frac{L_1}{R-t/2} $$

where $L_2$ is the length of the longer strip (at $R+t/2$) and $L_1$ the length of the shorter strip (at $R-t/2$), $t$ is the thickness of the strips. $R$ is the radius to the middle of the strips. Assumptions here are basically small bending and thin strips: $R\gg L_{1,2}\gg t$

Solving this equation for $R$ gives:
$$R=\frac{t(L_1+L_2)}{2(L_2-L_1)}$$

The change in length is related to the thermal expansion coefficients $\alpha_{1,2}$ and the change in temperature $\Delta T$ of the materials:

$$L_{1,2}=L(1+\alpha_{1,2}\Delta T)$$

Plugging this into the equation for the radius gives:
$$R=\frac{t}{\Delta\alpha\Delta T}$$

where $\Delta\alpha = \alpha_2-\alpha_1$ and a small term $\propto \Delta T$ has been neglected.