Two large parallel plates face each other across a vacuum. Both behave as black bodies; one is kept at $600\ \text{K}$ and the other at $300\ \text{K}$. A thin black metal sheet is placed between them, parallel to both, as shown in the figure, and heat passes only by radiation. In the steady state, what is the temperature of the sheet?

Fig. 1: Two large parallel black plates seen edge on, the left one at 600 K and the right one at 300 K, with a vacuum between them and a thin black sheet in the middle, parallel to both. The sheet's temperature is marked T with a question mark.