In a simple word, yes, but not the way human beings do. A dog does not have sweat glands in their skin or in their armpits the way we do. They sweat through the pads on the bottom of their feet.
Apocrine glands in humans produce sweat but in dogs those same glands secrete the pheromones that give the dog it’s own peculiar odor. It also helps seal the outer layer pf the skin, but it doesn’t produce sweat. The eccrine glands in a dogs paws release a substance much like human perspiration. Nerves, stress and heat can cause the release of that water like substance and the dog may leave behind damp paw prints as they walk.
The sweat glands they do have in the paws of their feet do not cool them down sufficiently so they pant. Panting helps them breath out excess heat from their bodies.
Like human beings dogs lose water when they sweat and it is important to keep them hydrated the same way we need to keep fluids in us on hot days or when we exercise. Keep bowls of cool fresh water both inside and outside the house. Don’t put it in the sunshine as it will warm it up and not provide the relief the dog needs. Instead put it in a shady spot under a tree or on in the shade of your house or other building. Make sure you keep refreshing it.
Be aware that when you leave a dog in a car , the temperatures inside the car are hotter than outside even on days where the temperatures outside are not excessive. Even with the windows cracked for ventilation the car can be too hot for the dog. It is better to leave them home than in a hot car. In some places there are now laws that protect animals from this. You can be fined for leaving a pet in your car unattended the same way you would be for leaving a small child alone.
Some breeds of dogs are more susceptible to the heat and heat stroke than others. Dogs with short pushed faces like the boxer, bulldog or pug have smaller airways than other dogs so it is more difficult for them to pant to release and blow out the excess heat in order to cool themselves.
Dogs with shorter legs have to work harder to walk or run so they may tire more easily from the heat.
You should realize that dogs are wearing fur coats in all weather. You wouldn’t put on a fur coat and go for a walk in the heat of the day, so don’t expect your dog to either. Take them for walks or exercise them during the cooler parts of the day. If you are out when it is hot and see your dog panting excessively try wetting their paws with a hose or in another water source. Some dogs love to play in water to cool themselves off on a hot day, the same way we do.
If you feel hot, chances are so does your dog and since they have a more difficult time cooling off, make sure you take care of their needs on hot days or in a hot environment.