The other thing is that if you're making five or six cups, there's a fair amount of volume of liquid, so it won't cool as quickly.Dumb French press question as I have never used - if you let the coffee steep for 4-7 minutes, doesn't that cool off the coffee? I ask this because I like my coffee hot and cool gradually as I am enjoying it not cooling as I am making it.
While buellbrewer has proper insulated presses, a 'normal' borosilicate glass press will keep the coffee pretty hot for those minutes, especially if you preheat the glass with a couple of cups of boiling water first.