Get a cooler beforehand, and get a bunch of heat packs. Experiment with them--see how many you need to get the temps in the cooler up to at least 85F, and how they change temperature as they age out.

You should be able to figure out how many you will need, and when to open them, so you can put the eggs in there to transport them on the move day. I personally would not suggest letting them drop to room temperature for 2 hours, keep them as close to incubation temperature as possible (never above it).