Let's see if I've got this right.
.257 Weatherby
Summer in the Nevada desert
5-6 shots with 2 minutes to cool between groups
I shoot in two of dumbest places for heat, the Arizona desert and Southern Georgia.

One is dry and hot the other is wet and hot but they are both hot.

Trying to shoot one gun for testing loads is fruitless unless you use cooling devices as mentioned above. I prefer to not drench my rifles in water or alcohol to aid in cooling.
- I try to coordinate my sessions for early AM testing, obviously the coolest part of my days. So getting up at o'dark thirty is part of the price I pay to get to my test range early enough.
- I bring 5 or 6 rifles which promotes longer down times allowing the preceding rifles to cool longer. If you don't have enough rifles, bring a .22 pistol and a Ruger 10-22 for some fun between.
- I use a pop up tent for shade and bring coolers with ice for cold water if necessary. I found a couple of nice high volume battery operated fans at Home Depot.
- I have a collapsible rifle rack to keep the barrels vertical and I leave the bolts out.
Life isn't fair but when you get lemons, make lemonade!

OOPs! I forgot to add that you should try a couple of different powders:
Norma 217
Retumbo
H-1000
These three are cooler burning but fill the case and yield decent velocities.