I ship in polyfoam (like the kind in your sofa cushions) which goes into a sealed box, then that gets put in another cushioned box. There's enough insulation with dividing barriers to do fairly well for any stints these are exposed to the outdoor temps- and I say that in a balmy 7˚.
The real damage comes during your local delivery. They bounce around all day in a cold milk-carton-looking delivery truck until it's your house, then they may get left outside!
I used to always mark to hold for pickup, but some POs ignore it no matter what. When I print out my labels now, I use the POs software's HOLD service, which DOESN'T PRINT the street address of the recipient, but rather the street address of the PO, so it CAN'T get delivered against your wishes. It also lets me enter an email so the recipient gets updates along the way, so they don't have to rely on the PO calling them- they get an email when it arrives.
This is the best way to handle non-compliant carriers, by far! After the crazy heat of the last few summers, I'm glad this is now available...I've had folks who got eggs that were developing when they arrived due to heat- they were still alive...but I don't want either extreme temps to hit the eggs if I can help it.
Off to suit up in my insulated overalls and North by Honeywell blue/black gloves. If you have cold climates, look these things up. You'll thank me later.
Where do you get your poly foam from to ship your eggs in?