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12:53
@Vashu this site:

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html

Gives me 6.66×10^6 joules/second emissions from a black body at 3694K and surface area of 0.6309 square meters.

time dilation would speed incident energy up from the point of view of the sphere which would make it faster/more extreme but rounding off to 7 hours...

2.613×10^11 J / 25200 gives us 1.03× 10^7 joules/second.

Comfortably higher than the 6.66×10^6 needed to reach the melting point of tungsten.

Note that tungsten isn't a perfect radiator so the difference may be larger.
Note: the above is without time dilation. with time dilation the incident energy would be about 70x or about 7.21 × 10^8 joules/second.... ish.

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