This is a heat conduction problem involving a symmetric network of identical rods. Since all rods are identical, their thermal resistance is equal. The system is symmetric about the central axis through B and C. Therefore, points B and C are at the same temperature, and no heat flows between them. We can thus treat the network as two parallel paths from A to D.

The effective resistance from A to D is calculated from the parallel combination: $\frac{1}{R_{\text{eff}}}=\frac{1}{2R}+\frac{1}{2R}=\frac{1}{R}$, so $R_{\text{eff}}=R$.

The total temperature difference is $200°C-20°C=180°C$. The temperature drop from A to B is half the total drop across the effective resistance R, because the path A-B-D has a resistance of 2R. Therefore, the temperature at B is $200°C-\frac{180°C}{2}=110°C$.

Final Answer: 110