We live in the high desert of Northern Nevada and it has not been hot for some months. I have not tried to wash the eggs off, but did pull some of the whitish material off.
I have not been able to determine which chicken is laying the egg. Recently my neighbors three hens (Freedom Rangers I believe) decided to join my little flock. Apparently they have not been feeding the chickens, just letting them free range (during the winter). They started out with quite a few chickens and several ducks. These three seem to be the only ones that survived.
So I do not really mind them being with the flock. The Salmon Faverolles are very accepting birds and these 3 have assimilated pretty well. They are still skittish around me and I have not seen them in the nest boxes. Perhaps these eggs (2 so far) are theirs. I have found both on the ground, not in the nest boxes. They sure were hungry when they first started coming over and were pretty scrawny. They are looking pretty good now!