Fair warning, I've never used this method. That said, typically once fermentation has started you want to do whatever you can to limit the amount of oxygen that comes into contact with your beer. If you are adding more wort after fermentation has started, you are really just adding more yeast food. They are already alert and actively eating from your first wort, so they shouldn't need to be reactivated.
Personally, I would siphon the second wort into the first wort, keeping the end of the hose submerged in the the first wort to minimize splashing.
And yes, I would say that the second wort should be cooled to the first wort temp before combiining the two. If you don't you may stress the yeast.
I'm not crazy. My mother had me tested.