Thanks everyone for the great replies.
After fiddling a bit with .5 degree changes up and down, I think I have now settled for 88 degrees air temp, next to the eggs. This is giving me readings of around 90 on the eggs surface using the temp gun, so I feel that's a good compromise.

I did calibrate the probed thermometer before using it. I calibrated 3 of them and chose the one that got closest (+0.2) to go inside the box.
The temp gun might be off, but I had compared temps between them before and they were much closer.

Right now I am guessing they do emit a little bit of heat, and the rest is probably due to error in measurement.

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