Areas that have an infection going on can feel hot. Birds can lay eggs at any time, there does not have to be a mating for a female to do so, without a physical exam the vet is exploring all possibilities for what might be causing the problem.
Egg binding is a very serious and dangerous issue, here is some additional info we have on the site Egg Binding: How to Prevent/How is it Treated? See if you can locate a wildlife rehab facility or a zoo with a vet that looks after the birds there, maybe they can help you.
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If you do not want to do x-rays, ask the vet what he/she thinks the possible issue might be and how it can be treated? Here is some info on what the exam should include The Avian Physical Examination
Take list of questions with you and make sure you ask what the side effects of any meds that might be prescribed will be.