It's unlikely to be a problem in the cold (though it could depend how cold), but heat can be a very different matter. My dog (though admitedly he's an extreme example) cannot walk longer than about 15 minutes in the sun if it's warmer than about 20 degrees (celsius). He cannot cool himself, has trouble breathing, and has to sit down. In the cold - well, I've yet to see it get too cold for Henri.
The problem with brachycephalic breeds is that their temperature regulation is extremely inefficient - and that's in a mammal that's already inefficient, whatever the breed. Dogs cool themselves by air only (no sweat glands, except inside the mouth and on the pads of feet) - and in the first instance, that means inside the nasal cavity. Well, a flat-faced breed doesn't have a large nasal cavity, so he's 'handicapped' already compared to longer nosed breeds. The next step in cooling is panting - and an expanding tongue to try to increase the surface area over which cool air can run. In a brachycephalic breed though, that can restrict the airway. And being a deep chested breed, they're usually not especially easy to cool anyway. Sooo - there are a load of factors there conspiring against this breed's ability to keep themselves cool, that don't affect longer nosed and shallower-chested breeds. The end result is a dog that has trouble cooling himself and hence is more vulnerable to heat. You may find that you need to exercise him a bit later on when it's cooler.