Meat and dairy

When does a pot/pan lose its status of a kli rishon? When it’s temperature drops below yad soledet?

I had a frying pan (was used for meat in the past 24 hours) which was clean that I used to fry eggs. I left it on the turned-off stove and accidentally slid the eggs onto a dairy plate. Is there an issue with eating the eggs ? Would this be an issue even if it was yad soledet?

What was the plate made out of

Glazed ceramic with metal patterns on top. The food was also not so hot

  1. Yes

  2. The eggs are ok to eat. The plate is ok.