Sorry for the delayed reply.
Yes, it might be the reason in your case. I think the power that you want to extract from Face F may not be possible so that’s why your problem converged at lower output heat of 0.01W but not on 1W. If the temperature is negative in kelvin on the wall, it means that it is approaching absolute zero. If you extract heat from the solid wall and the temperature indicates the negative in kelvin, then it might be a possibility that the wall has reached absolute zero and the entropy of the system is zero.
Generally, we refer to kelvin as an absolute zero, which means the vibration of the molecules in the system has stopped. We generally don’t go lower than zero kelvin. In some research cases, they talked about the negative kelvin temperature, but here I don’t think it’s applicable in your case. We keep this discussion simple here and I think your assumption may be correct about the power output is much higher than the power radiation can give. You should probably try to change the temperature value of the wall and heat flow, and then you can verify the behaviour.
My above observation depends upon the data that you have provided. Please let me know what you have observed in this simulation.