Doesnt need to be welding continuous to get hot.
And if you blow on a hot iron....does it cool it down ? The gas in the torch has almost zero cooling effect. The torches do just get warm during use, and with a lot of welding can get too hot to hold.
As said earlier. AC welding uses huge amounts of current....that means a lot of heat electrically. You could upgrade to a water cooled torch, but for DIY it really isnt necessary