Simple thermal radiation situation yields very different result from black body equation!?

The result for the steady-state temperature (modeling it numerous different ways) is consistently T=364 K. But the result according to Power=s*e*A*T^4 should be T=314.63 K when I use:

A=Area=1m^2 (modeled as a solid or as a surface sphere using shell elements)

e=emissivity=1.0

Power=power generated within Sphere= 1000W

The assumption is this is a sphere in space that does NOT have any solar flux adding heat to it.

Why is the answer so different from theoretical? I'm needing to use thermal radiation for the first time for some space equipment and am wondering whether there is a way to do things that will yield correct results for radiation. 

Thanks.

I am using Creo 11.0