You can do whatever you wish. If they started incubation at the same time they should hatch pretty close to together. If other hens are adding eggs to the nest so incubation does not start at the same time you will get a staggered hatch, which means they will hatch days apart. That adds a lot of stress to you and usually means you do not get a good hatch.
If you want chicks I'd collect fresh eggs and start them all at the same time. Or mark the eggs under the broody hen and leave them there. Mark them and remove any that don't belong. When you get a broody start all of the new eggs in the incubator at the same time.
If I understand your question, do not let the eggs that have started cool off. Put them straight in the incubator.