I have a small infrared thermometer bought to measure the electric motor temperature on an RC car. Something along the lines (but not the same) as this:
https://www.ebay.com.au/itm/Non-Contact-Mini-Infrared-Thermometer-IR-Temperature-Measuring-Digital-LCD-S8Q2/292620488982?epid=8017719467&hash=item44218a5116:g:aNYAAOSw64xbNA58:rk:24:pf:0I was recently shooting 3 round load development groups with a 6.5 Creedmoor varmint barrel and taking a temperature reading once in a while.
Before firing, the barrel was around 26 degrees, around the outside temperature. After 3 warm up shots it read ~29 degrees, which was surprising as I thought it felt warmer than that.
Subsequent loads would get up to 40 degrees, which felt quite warm to the touch, again felt warmer than the reading. I'd let the barrel cool to read 35-36 degrees and worked through the remaining groups within that window.
Google suggests that 42 degrees is the lower end for the onset of the threshold of pain, so maybe the reading was accurate.