I would imagine they'd have considered pyothorax - chest infection with fluid around the lungs. One of my cats had this 7 years ago and the first symptom was laboured breathing - she had to have her chest drained twice in 2 weeks, then was on antibiotics for another month, but she made a full recovery. I'm surprised they didn't do any testing on the fluid.
If it's not heart disease then I'm afraid FIP is another strong possibility - the high temperature would fit with that too.

I hope you get some answers soon.

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