Cat panting. What to do?

In the last week or so my cat has started panting after we take him outside on his leash. It usually starts once we take him inside. Then he will pant for a couple of seconds before stopping.  

It's only happened twice but I'm really worried about it. He's a british shorthair so he has a really dense coat, but I'm not sure if that has anything to do with it.

It's gotten really hot this past week, with temps reaching 80+ degrees. I've decided not to take him outside until it gets colder again, but It's hard because he really likes being outside in the heat. He's constantly meowing at the door for us to go outside with him. 

I thought cats were good at handling warm weather so I'm a bit confused by this whole thing. Could it be something else? Like an allergy that gets worse when it's hot?

He recently turned a year old so next week we'll take him to the vet for a check-up and booster shots. I'll ask her about it then, but I'm just wondering if there's anything I can do to make it easier on him now? 

Cats usually pant for two reasons, heat and nervousness. The clue in your post stated it has been above 80 degrees, so I am guessing it is from the heat. I have 5 cats and when outdoors, one always pants and none of the others do, so some are just  not as tolerant of heat. As long as it is not for an extended amount of time, say over ten minutes, and the cat is offered cool water, I would not be concerned, it is one of few ways the cat has to cool itself. If the cat struggles to breathe and becomes somewhat unresponsive, immerse in COOL water, not cold, (it is too much of a shock for the system) and contact your vet. For now until your vet visit, just observe him  and don't let him over exert  himself outdoors, just like a child they tend to not notice when they are getting too hot. Maybe try to let him explore in the shade, or take him out early in the day before it gets too hot, I take mine out at 6:00 AM and make sure they are in by noon., but we are in the hundreds here. All the luck!