The question is flawed if it is written as your post as the 1.6W/M^2/K implies that this thermal conductivity is based on an existing wall thickness. Do you have any idea what thickness this is based upon.
Also the temperature in Room A at 523 I assume is kelvin (ie 250C)
The ignition temperature of Room B at 238 I assume is not kelvin (approx. -35C)
I know this has not answered your question but I think more information is needed.