The 48qt coolers I’m familiar with have a fairly high spigot, you can tip the cooler to eliminate most of the dead space and capture more runnings.
The specific heat of your cooler assumes the cooler is not pre heated. You can not preheat the cooler, and overheat your strike water...or most prefer to add strike water 10-15 high and allow it to preheat the tun, then when strike water cools to strike temp the cooler is preheated and you mash in...either way works, the latter can be simpler and more accurate ime.