Every pet is different on the temperature they can endure. Older or overweight dogs, and brachycephalic (short nosed dogs such as bulldogs) are at greater risk for heat stroke and heat exhaustion which are life threatening. Dogs that are recently moved to a different climate and were previously not acclimated to heat will struggle and may always be more sensitive to high temperatures. The thickness of the coat doesn't necessarily matter. Even those with short, thin coats can become overheated.
MYTHBUSTER: Cats do NOT tolerate heat! They are just as susceptible to heat stroke as dogs and people.
Signs of heat exhaustion in cats are rapid breathing, redness of the tongue, vomiting, lethargy, stumbling, staggering gait. As their body temperature rises, the cat will collapse and have seizures or slip into a coma.
Vigorous exercise in high temperatures can bring on heat exhaustion or stroke especially when the dog is not used to vigorous exercise or the temperatures have suddenly changed from cold or cool to very warm.
Always bring plenty of water along for the dog when you go to a park or take the dog for a walk on a hot day. Pet stores have refillable drinking bottles for dogs. Dehydration can add to the danger of heat exhaustion and stroke.
In warm weather, their water bowl will need to be filled more often as they will go through their water much faster than previously and running out of water in warm temperatures can be life threatening.
Symptoms of heat exhaustion are lethargy and listlessness, excessive panting, and anxiety followed by diahrrea and vomiting which is followed by going into shock. Do NOT put cold water or ice packs on the animal because it makes it harder for them to cool off. Dogs cool themselves through shade, drinking water, and panting.
Source: Texas A&M College of Veterinary Medicine
Pet Safety: Heat Stroke