I googled this yesterday for a person in my bulldog seizure group and this is what I found. There are several reasons why it could be happening. If it's not heat related it could be
obesity (any extra weight)
A member had this to share....Our first bully, Tonka, started panting for, what we thought, was no reason. He would pant, while our second bully, Mack, would not. He didn't do it all the time but it did get progressively worse.
We kept the house like a meat locker, always kept fresh water with ice cubes in his bowl, had the fans going all the time, had a fan directly on him, we even bought our SUV because it had rear air and his comfort was a factor etc...we couldn't figure it out and neither could our vet. It didn't seem like a big thing because he seemed so healthy and we thought he was just hot natured.
Fast forward, I'm not exactly sure how long it was but we ended up, at the ER Vet, Tonka was panting like crazy and his tummy was protruding (it was filling with fluid).
To make a long story short, over the next 3 weeks my husband and I tried to move heaven and earth, went back and forth numerous times to UGA and GVS but ultimately lost our boy.
Tonka had a slow growing chondrosarcoma that they believe started in his trachea, and as it grew, eventually started putting pressure on his heart and finally infiltrated it. We lost him during the biopsy procedure
The tumor was sneaky, he never had any issues except for the panting, never showed up on any x-rays and even during the 3 weeks we tried to save him, was extremely difficult to see because of their build. I think if we had known to, maybe look in that direction we may have caught it before it was too late.
We now have complete body ultrasound and x-rays, done every 8-10 months, for both our boys. If something is there, we want to know right away.
This may not be your situation but maybe have someone check his heart
So if you can't find a reason and it won't stop, please consider asking your vet for help. Keep us updated!