I'm more interested in my barrel being a similar temp from shot to shot. What that temp is, is probably subject to debate, but I try to keep it warm but not hot to the touch. Its easy to reach up and touch it. The last range session began at 60 deg. It didn't take long to get up to warm to touch. Time spent recording velocity, POI AZ/EL, fishing the spent case out of my catcher, micro-dotting it, measuring ad recording CHG and placing it back where it came from in my ammo tray was sufficient to keep the temp from climbing too fast. It's more of finding a routine. When it's 80 and up, then the screaming hose monster comes with me.
Hot barrel related issues not necessarily in order of importance:
1)Pores in bore open up allowing contaminants to get a better hold.
2)Copper builds up faster (possibly due to #1)
3) Ouch!
4) If not cryogenically stress relieved, hot barrel may stray from true. A playing card thickness = 2 inches at 100 yds.
5) Mirage
6) As the round sits in a hot barrel, heat soaks through the thermally conductive brass into the powder, changing its characteristics.
7) Ouch again dammit!
Probably more but that's what comes to mind quickly.
Hoot