I beg and plead..properly chill these before and during serving.
A quick trip to the fridge and back won’t work. I’ve seen people use refrigerated wet towels placed under the dish to keep them cool. Ice packs may work as well if they are placed outside on a hot day.

Deviled eggs are something that I strongly associate with my grandmother and all my mom’s relatives, most of whom are now gone. Every time we had a family gathering with them when I was small, it seemed like there was a huge tray of deviled eggs. Now I never eat them and I never see them at social gatherings. Perhaps they are a vestige of another era. Though it does crack me up to see that Crate and Barrel sells a tray specifically designed for holding deviled eggs and a whole cookbook on deviled eggs. Maybe they are still the thing.