How old is he by the way...
I took Ares for a walk today (4 years old) and it was scorching out there...and we were in the sun the whole time. About half way through it, we both sat down in the shade for a break...usually about 2-3 minutes, he'll lay there and then he hops up and we get going again. Now a break should be something the owner decides is a good idea, not the dog.
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Boxers do hate the sun...anything over 75 and they can't have too much fun for too long.
Whatever you decide to do, don't get in the habit of carrying him back...actually, I'd say don't ever do it again. He can't learn that it's ok to stop walking when and where he pleases...or this may lead to a big problem.
Walks should be enjoyable for you and your boxer...so just remember that the more control you have, the more pleasant it is for you both.