Chill? Meh, I always figure the 5+ gallons of beer I'm about to dump on it will cool it down enough. I can wait weeks for a beer to ferment, but I cannot wait for 2 cups of liquid to cool down. I'm crazy like that.
Yeah , i just boil my sugar first then let it sit til i get to it in an hour during bottleing. Once you dump it in your bucket after sitting it is rapidly losing its heat with that surface area anyway.I would suggest giving it a stir quietly for a minute with the end of your racking hose and make shure your getting the swirling effect when racking. Just a peace of mind for a even mixing.
If necessary its really to quick cool your priming sugar solution in a bigger pan with cold ice water.If you set it in there is pretty much done way before you get through sanitizing your stuff.
5 oz is ok if as long as you get a full batch volume of bottles. That should be well carbonated.