Signs of heatstroke include:
Increased heart rate
Bright red tongue
Red or pale gums
Thick, sticky saliva
Vomiting (sometimes with blood)
As heatstroke progresses, it can cause seizures, coma, cardiac arrest, and death.
In the above video you see a police dog out working in the heat. The handler was able to recognize the signs and get the dog the emergency treatment it needed. It is important to realize that the signs may be hard to spot and the dog could still be trying to go after things or play with other dogs even though the internal body temperature reaches dangerous levels.