Hi there, you are through to Dr. Jake. Im a UK based vet. Im sorry to hear of your concerns with your cat, Copernicus.
His signs sound quite concerning . Rapid heavy breathing can be due to a few different conditions.
Its unlikely to be related to the heat unless he has been trapped in a car or under a car bonnet.
The most likely reasons for heavy breathing is a heart and or lung condition. The most common one we see in cats regarding the heart is heart failure due to thickening of the muscle of the heart, causing it to pump blood poorly, this results in fluid to build up on the lungs and the chest. This is an emergency and for this reason i would recommend getting an appointment with a vet straight away so they can examine him, listen to his heart to make sure there is no murmur and to listen to the chest to make sure no fluid can heard on the lungs
Feline asthma can cause heavy breathing though this usually shows as wheezing and coughing so id expect this is less likely.
Pain can also show as heavy breathing, unless your cat is showing signs of trauma - bleeding, bruising, limping then id expect again this is less likely, though trauma can also lead to collapsed lungs also.
As above, i would call the vets straight away for him to be examined
I hope all this information helps