Mine comes off the stove boiling, and goes into the bottling bucket just after it starts racking. Five oz. of sugar in 2 cups of water, even if boiling, can't affect the ultimate temperature of 5 gal of beer significantly.
“Malt does more than Milton can / To justify God’s ways to man”
-A. E. Housman (1859–1936). A Shropshire Lad , 1896.